# Trigonometric Function Word Problems

Many students find trigonometric functions word problems difficult. At TuLyn, we created word problems on trigonometric functions to help you better understand trigonometric functions.

### Tangent Word Problems

Practice tangent word problems.

### Sine Word Problems

Practice sine word problems.

### Cosine Word Problems

Practice cosine word problems.

### Cotangent Word Problems

Practice cotangent word problems.

### Cosecant Word Problems

Practice cosecant word problems.

### Secant Word Problems

Practice secant word problems.

### SOHCAHTOA Word Problems

Practice sohcahtoa word problems.

### Arcsine Word Problems

Practice arcsine word problems.

### Inverse Trigonometric Functions Word Problems

Practice inverse trigonometric functions word problems.

### Evaluating Trigonometric Functions Word Problems

Practice evaluating trigonometric functions word problems.

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Are you looking for trigonometric functions word problems? TuLyn is the right place. We have tens of word problems on trigonometric functions and hundreds on other math topics.

Below is the list of all word problems we have on trigonometric functions.

# Trigonometric Functions Word Problems

• A 10-ft ladder leans against a wall (#353)
A 10-ft ladder leans against a wall at an angle with the horizontal. The top of the ladder is x feet above the ground. If the bottom of the ladder is pushed toward the ...
trigonometric functions, functions
• A 25 m tower standing vertically (#847)
A 25 m tower standing vertically on a hillside casts a shadow down the hillside that is 27 m long. The angle at the tip of the shadow S, subtended by the tower is  26...
trigonometric functions, law of sines, sine, functions
• A 95-ft tree casts a shadow (#2396)
A 95-ft tree casts a shadow that is 45 ft ...
trigonometric functions, functions
• A crow is on the ground (#303)
A crow is on the ground 80 feet from the base of a 45 foot tall tree. It then flies straight through the air to the top of the ...
inverse trigonometric functions, trigonometric functions, functions
• A ferris wheel is built such that (#3414)
A ferris wheel is built such that the height (h) in feet above the ground of a seat on the wheel at time (t) in sec can be modeled by: H(t)=53+50sin(π/10t-π/2)
Find the angular speed in radians and the linear speed in feet?
sine, trigonometric functions, functions
• A ladder 39 feet long leans against a building (#1419)
A ladder 39 feet long leans against a building and reaches the ledge of a window. If the foot of the ladder is 15 feet from the foot of the ...
trigonometric functions, cosine, right triangles, pythagorean theorem, triangles, polygons, shapes, plane figures, curves, functions
• A ladder leans against a building forming an angle (#2635)
A ladder leans against a building forming an angle of 50 degrees with the ground. The base of the ladder is 8 feet from the ...
cosine, trigonometric functions, functions
• A ladder rests against a wall (#2926)
A ladder rests against a wall. the top of the ladder reaches 15 feet up the wall, and makes an angle of 53 with the ...
sohcahtoa, trigonometric functions, trigonometric identities, functions, identities
• A man on a 135-ft vertical cliff looks down (#2873)
A man on a 135-ft vertical cliff looks down at an angle of 16 degrees and sees his friend. How far away is the man from his ...
pythagorean theorem, sohcahtoa, trigonometric functions, trigonometric identities, right triangles, plane figures, triangles, curves, shapes, polygons, functions, identities
• A mass suspended from a spring (#2213)
A mass suspended from a spring is pulled down a distance of 2 feet from its rest position. The mass is released at time t=0 and allowed to oscillate. If the mass returns to this position after 1 ...
trigonometric functions, functions
• A pig at Papas Barn just had a litter of piglets (#2809)
A pig at Papas Barn just had a litter of piglets. The whole barn is about 12 miles long. In the middle of the night one piglet ran out of the barn a traveled down to the Bray Ranch which is about 13.5 miles away. When viewed on the towns map the two barns make a 115 degree ...
law of sines, sine, trigonometric functions, functions
• A pilot flies in a straight path (#2327)
A pilot flies in a straight path for 1 hour and 30 minutes. She then makes a course correction, heading 10 degrees to the right of her original course, and flies 2 hours in the new direction. If she maintatins a constant speed of 620 miles per ...
trigonometric functions, functions
• A plane flies 1.3 hours at 110 miles per hour (#2029)
A plane flies 1.3 hours at 110 miles per hour at a bearing or North 40 degrees East. It then turns and flies on a bearing of South 50 degrees East at the same rate for 1.5 hours. How far is the plane from the starting ...
trigonometric functions, functions
• A ramp is at an angle of elevation (#1987)
A ramp is at an angle of elevation of 30 degrees. The distance from the top of the slope to the ground is 900 ...
trigonometric functions, trigonometric identities, sohcahtoa, functions, identities
• A satellite, travelling in a circular orbit (#253)
A satellite, travelling in a circular orbit 700 km above Earth, will pass directly over a tracking station at noon. The satellite takes 95 mins to complete an orbit.
a) If the antenna for a tracking station is aimed at an angle of elevation of 30 degrees, at what time will the satelite pass through the beam of the ...
law of sines, sine, trigonometric functions, functions
• A ship at sea, the Admiral, spots two other ships (#3031)
A ship at sea, the Admiral, spots two other ships, the Barstow and the Cauldrew and measures the angle
between them to be 65° . They radio the Barstow and by comparing known landmarks, the distance
between the Admiral and the Barstow is found to be 236 meters. The Barstow reports an angle of 36°
between the Admiral and the Cauldrew. To the nearest ...
sine, trigonometric functions, functions
• A ski slope at a mountain has an angle of elevation (#2257)
A ski slope at a mountain has an angle of elevation of 25.2 degrees. The vertical height of the slope is 1808 ...
sohcahtoa, trigonometric functions, trigonometric identities, functions, identities
• A straight road makes an angle of 15 degrees (#2414)
A straight road makes an angle of 15 degrees with the horizontal. When the angle of elevation of the sun is 57 degrees, a vertical pole at the side of the road casts a shadow 75 feet long directly down the ...
law of sines, sine, trigonometric functions, functions
• A straight road slopes upward (#2765)
A straight road slopes upward at 15 degrees from the horizontal. How long is the section of the road that rises a vertical distance of 250 feet? ( Express the answer to the nearest 10 feet.)
cosine, trigonometric functions, functions
• A train is traveling up a slight grade (#2315)
A train is traveling up a slight grade with an angle of inclination of only 2 ...
cosine, trigonometric functions, functions
• A tree on a hillside casts a shadow (#1959)
A tree on a hillside casts a shadow 215 ft down the hill. If the angle of inclination of the hillside is 22 degrees to the horizontal and the angle of elevation of the sun is 52 ...
sine, trigonometric functions, functions
• Amelia sees a jet heading south away from her (#2876)
Amelia sees a jet heading south away from her at 42 degree angle of elevation. Twenty seconds later the jet is still moving away from her, heading south at a 15 degree angle of elevation. If the jets elevation is constantly 6.3 ...
sohcahtoa, trigonometric functions, trigonometric identities, functions, identities
• An airplane flying at an altitude of 6 miles (#2080)
An airplane flying at an altitude of 6 miles, is on a flight path that goes directly over you. If angle is the angle of elevation, find the distance from the observer to plance at 30...
trigonometric functions, functions
• An airplane is sighted at the same time (#54)
An airplane is sighted at the same time by two ground observers who are 4 miles apart and both directly west of the airplane. They report the angles of elevation as 11° and 22°...
law of sines, sine, trigonometric functions, functions
• An airplane takes off from a field (#2717)
An airplane takes off from a field with an 8 degree angle with the horizontal ...
trigonometric identities, trigonometric functions, sohcahtoa, functions, identities
• An antenna is atop of a 80 foot building (#2190)
An antenna is atop of a 80 foot building, 12 feet from the edge. From a point 60 feet from the base of the building, the angle from the ground level to the top of the building is 68 ...
trigonometric functions, functions
• At noon, a tree having a height of 10 feet (#2695)
At noon, a tree having a height of 10 feet casts a shadow 15 feet in length. Find, to the nearest ...
trigonometric functions, functions
• Coast Guard Station Able is located (#2381)
Coast Guard Station Able is located 150 miles due south of Station Baker. A ship at sea sends an SOS call that is received by each station. The call to Station Able indicates that the ship is located N55°E; the call to Station Baker indicates that the ship is located S60°E.
(a) How far is each station from the ship?
(b) If a helicopter capable of flying 200 miles per hour is dispatched from the nearest station to the ...
sine, law of sines, trigonometric functions, functions
• cosine (#78)
AB=1000 straight N and turn 127 degree to the ...
cosine, trigonometric functions, functions
• Cosine (#10153)
Three ships a b and c are anchored in the ocean. the distance from a to b is 25.5 km, from b to c is 17.2 km and from c to a is 37.4 ...
cosine, trigonometric functions, functions
• Due to wind, a tree grew (#1110)
Due to wind, a tree grew so that it leaned 8 degrees from the vertical. From a point on the ground 28 meters from the base of the tree, the angle of elevation to the top of the tree is 24.6 ...
law of sines, sine, trigonometric functions, functions
• During an air show, a stunt pilot flies (#3384)
During an air show, a stunt pilot flies over a crown at an altitude of 2500 feet. One minute later the angle of elevation of the plane is 15 ...
trigonometric functions, functions
• Frank is standing 110 yards from (#30)
Frank is standing 110 yards from 32-yard high ...
cosine, trigonometric functions, functions
• From a glider 200 feet above the ground (#2159)
From a glider 200 feet above the ground, two sightings of a stationary object directly in front are taken 1 minute ...
trigonometric functions, functions
• From a point on the ground (#2553)
From a point on the ground, a person notices a 110-foot antenna on the top of a hill subtends an angle of 1.5 deg. If the angle of elevation on the bottom of the antenna is 25 ...
trigonometric functions, functions
• From an airplane, Janara looked down (#1039)
From an airplane, Janara looked down to see a bit. If she looked down at an angle of 9 degrees and the airplane was half a mile above the ...
law of cosines, cosine, trigonometric functions, functions
• From the top of a lighthouse (#1560)
From the top of a lighthouse 160 feet above sea level, the angle of depression to a boat at sea is 25 degree. To the nearest ...
trigonometric identities, trigonometric functions, sohcahtoa, functions, identities
• High tide at Fisherman`s Cove occurs (#2942)
High tide at Fisherman's Cove occurs at 3am and is 2.1m. Low tide occurs at 9am and is 0.7...
cosine, trigonometric functions, functions
• If you let 100 feet of string out (#3278)
If you let 100 feet of string out on a kite and fly it how high can the kite go?
sohcahtoa, trigonometric functions, trigonometric identities, functions, identities
• In high school baseball, the front of the pitcher`s rubber (#3395)
In high school baseball, the front of the pitcher's rubber is 60.5 feet away from the back end of the home plate, and the first base bag is 90 ft fromhome place. The home plate and each of the bases makes a 90 degree angle with the next one, and the pitcher's rubber is aligned between home place and second ...
trigonometric functions, functions
• Island A is 230 miles from island B (#3030)
Island A is 230 miles from island B. A ship captain travels 270 miles from island A and then finds that he
is off course and 180 miles from island B. What angle, in degrees, must he turn through to head straight
for island ...
sine, trigonometric functions, functions
• Law Of Cosines (#6617)
A flagpole 20ft. high was suited at the top of a hill. A string was tied from the top of the pole to the point P on the ground 150m. from the foot of the pole. If the flagpole measured an angle of 100 degree with the surface of the ...
law of cosines, cosine, trigonometric functions, functions
• Law Of Cosines (#9337)
A flashlight was focused on the mirror forming an angle of 80 degrees. The length of the light from the flashlight to the mirror was 8 meters and the lengthof the reflected light to the wall was 7 ...
law of cosines, cosine, trigonometric functions, functions
• Law Of Cosines (#9610)
Grandpa Violente wishes to find the distance between two points A and B on the opposite side of the river. On his side of the river he locates two trees that are 472 feet apart at C and D. He measures the angles w=17, x=66, y=59 and z=20, as ...
law of cosines, cosine, trigonometric functions, functions
• Law Of Sines (#6240)
a pilot is flying over a straight highway. The angles of depression are 5 miles apart and are 32 degees and 48 ...
law of sines, sine, trigonometric functions, functions
• Law Of Sines (#6872)
AB is a line 652 feet long on one bank of a stream, and C is a point on the opposite bank. A = 58 degrees, and B = 48 degrees ...
law of sines, sine, trigonometric functions, functions
• Law Of Sines (#8003)
A rocket tracking station has two telescopes A and B placed 1.1 miles apart. The telescopes lock onto a rocket and transmit their angles of elevation to a computer after a rocket ...
law of sines, sine, trigonometric functions, functions
• Law Of Sines (#8022)
A pilot is flying over a straight highway. He determines the angles of depression to two mileposts, 9 mi apart, to be 32° and 48°, as shown in the figure. Round your answers to the nearest tenth mile.

(a) Find the distance of the plane from point ...
law of sines, sine, trigonometric functions, functions
• Law Of Sines (#8162)
A boat is sailing due east parallel to the shoreline at a speed of 10 miles per hour. At a given time the bearing to the light house is S 70 degrees W and 15 minutes later the bearing is S 63 ...
law of sines, sine, trigonometric functions, functions
• Law Of Sines (#8590)
The pentagon has 5 side each of them are 921 feet ...
law of sines, sine, trigonometric functions, functions
• Law Of Sines (#9481)
to find the distance from the house at A to the house at B, a surveyoor measures the anges BAC to be 40 degrees and then walks off a distance of 100 feet to C and measures the angle ACB to be 50 ...
law of sines, sine, trigonometric functions, functions
• Law Of Sines (#9857)
A tree growing on a hillside casts a 157ft shadow straight down the hill. Find the vertical height of the tree if relative to the horizontal, the hill slopes 11...
law of sines, sine, trigonometric functions, functions
• Law Of Sines (#10520)
A 25 m tower standing vertically on a hillside casts a shadow down the hillside that is 27 m long. The angle at the tip of the shadow S, subtended by the tower is  26. What is the angle of elevation of the sun at S
law of sines, sine, trigonometric functions, functions
• Law Of Sines (#10808)
To find the length of the span of a proposed ski lift from A to B, a survey or measures the angle DAB to be 25 degrees and then walks off a distance of 1000ft to C and measures the angles ACB to 15 ...
law of sines, sine, trigonometric functions, functions
• Liselle is flying her kite (#2001)
Liselle is flying her kite with 62 feet of string attached to the ground. She measures 5 feet of string from the ground to a point of 4 feet ...
trigonometric functions, sohcahtoa, trigonometric identities, functions, identities
• Natali is 5 feet 3 inches tall (#2200)
Natali is 5 feet 3 inches tall. She walks from the base of a broadcasting tower directly toward the tip of the shadow cast by the tower. When she is 130 feet from the tower and 3 feet from the tip of the tower's shadow, her shadow starts to appear beyond the tower's ...
trigonometric functions, functions
• Sine (#5747)
bob and donna leave their home .they travel in opposite drections. bob travels 65 mph and donna travels 75 mph ...
sine, trigonometric functions, functions
• Sine (#9299)
a ship is sailing toward a small island 800 miles away. if the ship is 2 degrees of course, by how many miles will it miss he island
sine, trigonometric functions, functions
• SOHCAHTOA (#3275)
The angle of elevation from point A to the top of a cliff is 38 ...
sohcahtoa, trigonometric functions, trigonometric identities, functions, identities
• SOHCAHTOA (#6816)
two towers a and b are located 48 m apart. Rod who is standing at the base of tower B found that the angle of elevation of tower a is twice the angle elevation of tower B as observed by Alexandra who is also standing at the base of tower \"A . At a point midway between their bases the angle elevation of two towers are complementary ...
sohcahtoa, trigonometric functions, trigonometric identities, functions, identities
• SOHCAHTOA (#8192)
a yard stick, held vertically on a level surface, cast a show 1 foot 8 inches ...
sohcahtoa, trigonometric functions, trigonometric identities, functions, identities
• SOHCAHTOA (#8230)
An advertising blimp hover over a stadium at an altitude of 125m. The pilot sights a tennis court at 8 degree angle of ...
sohcahtoa, trigonometric functions, trigonometric identities, functions, identities
• SOHCAHTOA (#8231)
An advertising blimp hover over a stadium at an altitude of 125m. The pilot sights a tennis court at 8 degree angle of ...
sohcahtoa, trigonometric functions, trigonometric identities, functions, identities
• SOHCAHTOA (#8540)
From the top of a barn 25 feet tall, you see a cat on the ground. The angle of depression of the cat is 40 degrees. How many feet, to the nearest ...
sohcahtoa, trigonometric functions, trigonometric identities, functions, identities
• Tangent (#8579)
Using unit circle ...
tangent, trigonometric functions, functions
• Tangent (#8597)
Using unit circle properties,  find the value of tan ( - 11 pi / 6 )
tangent, trigonometric functions, functions
• The course for a bike race follows (#3069)
The course for a bike race follows a triangular shaped trail. The first leg is a straight 6 kilometre ride. After that, the biker must turn 283 degrees to the left and follow the train to the next turn. Turning 269 degrees again to the left will take the biker to the finish line, which is exactly where he ...
law of sines, sine, trigonometric functions, functions
• The diagonal of a rectangle (#2211)
The diagonal of a rectangle is 25 and the angle formed by the shorter side and the diagonal is 71 ...
trigonometric functions, functions
• The length of a tree`s shadow (#2400)
The length of a tree's shadow is 15 m. The angle of elevation of the sun is 38 ...
trigonometric functions, functions
• The right angle of the triangle (#2489)
The right angle of the triangle is 1808 feet the slope is 25,2 ...
pythagorean theorem, right triangles, trigonometric functions, plane figures, shapes, polygons, curves, triangles, functions
• Trigonometric Functions (#2288)
If angle B = 25 degrees 30', angle A = 90 ...
trigonometric functions, functions
• Trigonometric Functions (#3778)
A mountain peak C is 4130 ft above sea level, and from c the angle of elevation of the second peak B is 5 degree. An aviator at directly over peak c, find angle CAB is 43.8 degree where his altimeter show that he is 8460 ft above sea ...
trigonometric functions, functions
• Trigonometric Functions (#4393)
a 10-ft ladder leans against a wall at an angle with the horizontal.The top of the ladder is x feet above the ground.If the bottom of the ladder is pushed toward the ...
trigonometric functions, functions
• Trigonometric Functions (#5807)
At a local airport, a light that produces a powerful white-green beam is placed on the top of a 45-foot tower. If the tower is at one end of the ...
trigonometric functions, functions
• Trigonometric Functions (#6254)
WATER LEVEL IN A HARBOR: the water level (in feet) in Boston Harbor during a certain 24-hr period is approimated by the formula:

H= 4.8sin Pi/6 (t-10) + 7.6 (0 < t < 24)

when t=0 corresponds to 12 am. When is the water level rising and when is falling? Find the relative extrema of H and interpret the results
trigonometric functions, functions
• Trigonometric Functions (#7204)
A tire with a 29.6 inch diameter traveling at a constant speed of 0.7 miles per hour over a nail at exactly 12 noon. The nail is stuck in the tire but does not deflate it.

a. What is the speed of the tire in inches per second rounded to the nearest hundredth?

b. How often does the nail hit the ground to the nearest hundredth of a second?

c. Write a cosine equation in the form y = Acos(B(x – C)) + D that calculates the height that the nail is above the ground for any given time. Makes sure that A, B, C, D are exact values.

d. How high above the ground will the nail be at:

i. 12:00:08 ii. 12:00:15

iii. 12:01 iv. 12:15

...
trigonometric functions, functions
• Trigonometric Functions (#8040)
A 50 foot tall tree casts a shadow that is 40 feet long. Draw a picture on your scratch paper, including the "ray of sunshine" causing the shadow. ...
trigonometric functions, functions
• Trigonometric Functions (#8119)
three times the sine of a certain in angle is twice of the square of the cosine of the same ...
trigonometric functions, functions
• Trigonometric Functions (#8927)
the short leg of a 30 degrees -60 dgrees -and 90 degrees triangle is 7.4 meters long.find the perimeter
trigonometric functions, functions
• Trigonometric Functions (#9286)
A water wheel with radius 2 m has 0.2 m submerged and rotates at 5 rev/...
trigonometric functions, functions
• Trigonometric Functions (#9303)
A ship is sailing toward a small island 800 miles away. If the ship is 2 degrees of ...
trigonometric functions, functions
• Trigonometric Functions (#9767)
In two minutes a plane descending at a constant angle of depression of 10.5 degrees travels 3800 m along its flight ...
trigonometric functions, functions
• Two firetowers are 30 kilometers apart (#2308)
Two firetowers are 30 kilometers apart, tower A being due west of tower B. A fire is spotted from the towers and the bearings from A and B are E 14 degreesN and W 34 degreesN, ...
trigonometric functions, functions
• Two observers 200 feet apart (#3346)
Two observers 200 feet apart are in line with the base of flagpole. The measurement of the angle of elevation of the top from one observer is 30 degrees and other 60 ...
trigonometric functions, functions
• Two observers,who are 2 miles apart (#1172)
Two observers,who are 2 miles apart on a horizontal  plane,observe a balloon the same vertical plane with themselves. The angles of elevation are 50' and 65' respectively. Find the height of the balloon ...
sine, law of sines, trigonometric functions, functions
• Two people leave from the same point (#2378)
Two people leave from the same point. Their paths diverge by 95 degrees. If one walks 5 miles and the other walks 3.5 ...
law of sines, sine, trigonometric functions, functions
• Two ships leave port at 4 p.m. (#1547)
Two ships leave port at 4 p.m. One is headed at a bearing of N 38 E and is traveling at 11.5 miles per hour. The other is traveling 13 miles per hour at a bearing of S 47 E. How far apart are they when dinner is served at 6 p.m.?
cosine, law of cosines, trigonometric functions, functions
• Tyler is flying a kite on 1700 feet of string (#2439)
Tyler is flying a kite on 1700 feet of ...
sohcahtoa, trigonometric functions, trigonometric identities, functions, identities
• While fishing, you spot a fish below the water (#2182)
While fishing, you spot a fish below the water at a 25 degree angle with the surface. It is producing air bubbles 20 feet ...
trigonometric functions, functions
• X and Y are two lighthouses (#2369)
X and Y are two lighthouses, Y being 20 Km due east of X. From a ship due south of X, the bearing of Y was 055 degrees. Find the distance of the ship from ...
trigonometric functions, functions
• You need to determine the length (#697)
You need to determine the length of a tunnel drilled through a lunar peak at the center of a crater. From a point on the crater floor, you run ropes to the ends of the tunnel. The first rope's distance covered is 24.5 meters and the second rope's distance is 21.2 meters. The two ropes meet at an angle of 68 degrees.
a) What is the length of the ...
law of sines, sine, trigonometric functions, functions

### Functions Word Problems

Find word problems and solutions on functions.