Deck 7: Applications of Trigonometric Functions

Question 1

Solve the right triangle using the information given. Round answers to two decimal places, if necessary.

Answer 1

D

Question 2

Solve the right triangle using the information given. Round answers to two decimal places, if necessary.

- $\mathrm { a } = 5 , \beta = 35 ^ { \circ } ;$ Find $\mathrm { b } , \mathrm { c }$ , and $\alpha$ .

A) $\begin{array} { l } \mathrm { b } = 4.5 \\\mathrm { c } = 7.1 \\\alpha = 55 ^ { \circ }\end{array}$
B) $\begin{array} { l } \mathrm { b } = 3.5 \\\mathrm { c } = 7.1 \\\alpha = 55 ^ { \circ }\end{array}$
C) $\begin{array} { l } \mathrm { b } = 4.5 \\\mathrm { c } = 6.1 \\\alpha = 55 ^ { \circ }\end{array}$
D) $\begin{array} { l } \mathrm { b } = 3.5 \\\mathrm { c } = 6.1 \\\alpha = 55 ^ { \circ }\end{array}$

Answer 2

$\begin{array} { l } \mathrm { b } = 3.5 \\\mathrm { c } = 6.1 \\\alpha = 55 ^ { \circ }\end{array}$

Question 3

Solve the right triangle using the information given. Round answers to two decimal places, if necessary.

Answer 3

B

Question 4

Choose the one alternative that best completes the statement or answers the question.
Find the exact value of the expression. Do not use a calculator.

Question 5

Choose the one alternative that best completes the statement or answers the question.
Find the exact value of the expression. Do not use a calculator.

Question 6

Two sides of a right triangle ABC (C is the right angle) are given. Find the indicated trigonometric function of the given
angle. Give exact answers with rational denominators.

Question 7

Solve the problem.

Question 8

Write the word or phrase that best completes each statement or answers the question.

Question 9

Two sides of a right triangle ABC (C is the right angle) are given. Find the indicated trigonometric function of the given
angle. Give exact answers with rational denominators.

Question 10

Two sides of a right triangle ABC (C is the right angle) are given. Find the indicated trigonometric function of the given
angle. Give exact answers with rational denominators.

Question 11

Choose the one alternative that best completes the statement or answers the question.
Find the exact value of the expression. Do not use a calculator.

Question 12

Two sides of a right triangle ABC (C is the right angle) are given. Find the indicated trigonometric function of the given
angle. Give exact answers with rational denominators.

Question 13

Two sides of a right triangle ABC (C is the right angle) are given. Find the indicated trigonometric function of the given
angle. Give exact answers with rational denominators.

Question 14

Two sides of a right triangle ABC (C is the right angle) are given. Find the indicated trigonometric function of the given
angle. Give exact answers with rational denominators.

Question 15

Two sides of a right triangle ABC (C is the right angle) are given. Find the indicated trigonometric function of the given
angle. Give exact answers with rational denominators.

Question 16

Two sides of a right triangle ABC (C is the right angle) are given. Find the indicated trigonometric function of the given
angle. Give exact answers with rational denominators.

Question 17

Two sides of a right triangle ABC (C is the right angle) are given. Find the indicated trigonometric function of the given
angle. Give exact answers with rational denominators.

Question 18

Solve the right triangle using the information given. Round answers to two decimal places, if necessary.

Question 19

Choose the one alternative that best completes the statement or answers the question.
Find the exact value of the expression. Do not use a calculator.

Question 20

Two sides of a right triangle ABC (C is the right angle) are given. Find the indicated trigonometric function of the given
angle. Give exact answers with rational denominators.

Question 21

Solve the problem.
John (whose line of sight is 6 ft above horizontal) is trying to estimate the height of a tall oak tree. He first measures the angle of elevation from where he is looking as 35°. He walks 30 feet closer to the tree and finds
That the angle of elevation has increased by 12°. Estimate the height of the tree rounded to the nearest whole
Number.

A) 67 ft
B) 86 ft
C) 61 ft
D) 90 ft

Question 22

Solve the problem.
A twenty-five foot ladder just reaches the top of a house and forms an angle of 41.5° with the wall of the house. How tall is the house? Round your answer to the nearest 0.1 foot.

A) 18.7 ft
B) 18.8 ft
C) 18.6 ft
D) 19 ft

Question 23

Solve the problem.
A radio transmission tower is 210 feet tall. How long should a guy wire be if it is to be attached 13 feet from the top and is to make an angle of 20° with the ground? Give your answer to the nearest tenth of a foot.

A) 614.0 ft
B) 209.6 ft
C) 223.5 ft
D) 576.0 ft

Question 24

Solve the problem.
A surveyor is measuring the distance across a small lake. He has set up his transit on one side of the lake 90 feet from a piling that is directly across from a pier on the other side of the lake. From his transit, the angle between
The piling and the pier is 55°. What is the distance between the piling and the pier to the nearest foot?

A) 74 ft
B) 63 ft
C) 129 ft
D) 52 ft

Question 25

Two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no
triangle at all. Solve any triangle(s) that results.

Question 26

Solve the problem.
A photographer points a camera at a window in a nearby building forming an angle of 42° with the camera platform. If the camera is 52 m from the building, how high above the platform is the window, to the nearest
Hundredth of a meter?

A) 0.9 m
B) 1.11 m
C) 46.82 m
D) 57.75 m

Question 27

Choose the one alternative that best completes the statement or answers the question.

Question 28

Solve the triangle.

Question 29

Choose the one alternative that best completes the statement or answers the question.

Question 30

Solve the triangle.

Question 31

Write the word or phrase that best completes each statement or answers the question.
Yosemite Falls in California consists of three sections: Upper Yosemite Fall (by itself one of the ten highest
waterfalls in the world), the Middle Cascade, and Lower Yosemite Fall. From a footbridge across the creek 2500
feet from the falls, the angles of elevation to the top and bottom of Upper Yosemite Fall are 45.74° and 24.42°,
respectively. How high is the total series of three falls? How high is Upper Yosemite Fall? Round your answers
to the nearest foot.

Question 32

Choose the one alternative that best completes the statement or answers the question.

Question 33

Solve the triangle.

Question 34

Solve the triangle.

Question 35

Solve the problem.
A building 200 feet tall casts a 40 foot long shadow. If a person looks down from the top of the building, what is the measure of the angle between the end of the shadow and the vertical side of the building (to the nearest
Degree)? (Assume the person's eyes are level with the top of the building.)

A) 78°
B) 11°
C) 12°
D) 79°

Question 36

Choose the one alternative that best completes the statement or answers the question.
A forest ranger at Lookout A sights a fire directly north of her position. Another ranger at Lookout B, exactly 2 kilometers directly west of A, sights the same fire at a bearing of N41.2°E. How far is the fire from Lookout A?
Round your answer to the nearest 0.01 km.

A) 2.32 km
B) 2.25 km
C) 2.18 km
D) 2.28 km

Question 37

Solve the problem.
A straight trail with a uniform inclination of 18° leads from a lodge at an elevation of 800 feet to a mountain lake at an elevation of 7,100 feet. What is the length of the trail (to the nearest foot)?

A) 7,465 ft
B) 22,976 ft
C) 20,387 ft
D) 6,624 ft

Question 38

Write the word or phrase that best completes each statement or answers the question.
In 1838, the German mathematician and astronomer Friedrich Wilhelm Bessel was the first person to calculate
the distance to a star other than the Sun. He accomplished this by first determining the parallax of the star, 61
Cygni, at 0.314 arc seconds (Parallax is the change in position of the star measured against background stars as
Earth orbits the Sun. See illustration.) If the distance from Earth to the Sun is about 150,000,000 km and

Question 39

Two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no
triangle at all. Solve any triangle(s) that results.

Question 40

Solve the problem.
A tree casts a shadow of 26 meters when the angle of elevation of the sun is 24°. Find the height of the tree to the nearest meter.

A) 10 m
B) 11 m
C) 12 m
D) 13 m

Question 41

Choose the one alternative that best completes the statement or answers the question.
Solve the triangle.

Question 42

Write the word or phrase that best completes each statement or answers the question.
A pier 1250 meters long extends at an angle from the shoreline. A surveyor walks to a point 1500 meters down
the shoreline from the pier and measures the angle formed by the ends of the pier. If is found to be 53. What acute angle (correct to the nearest 0.1) does the pier form with the shoreline? Is there more than one possibility? If so, how can we know which is the correct one?

Question 43

Write the word or phrase that best completes each statement or answers the question.
Two surveyors 180 meters apart on the same side of a river measure their respective angles to a point between
them on the other side of the river and obtain 5. How far from the point (line-of-sight distance) is each surveyor? Round your answer to the nearest 0.1 meter.

Question 44

Solve the triangle. Find the angles  and  first.

Question 45

Solve the problem.

Question 46

Solve the problem.
A rocket tracking station has two telescopes A and B placed 1.3 miles apart. The telescopes lock onto a rocket and transmit their angles of elevation to a computer after a rocket launch. What is the distance to the rocket
From telescope B at the moment when both tracking stations are directly east of the rocket telescope A reports an
Angle of elevation of and telescope B reports an angle of elevation of

A) 2.42 mi
B) 1.4 mi
C) 0.75 mi
D) 2.26 mi

Question 47

Choose the one alternative that best completes the statement or answers the question.
Solve the triangle.

Question 48

Solve the triangle. Find the angles  and  first.

Question 49

Solve the problem.
A ship sailing parallel to shore sights a lighthouse at an angle of from its direction of travel. After traveling 3 miles farther, the angle is . At that time, how far is the ship from the lighthouse?

A) 1.82 mi
B) 4.48 mi
C) 7.37 mi
D) 3 mi

Question 50

Solve the problem.
A ship at sea, the Admiral, spots two other ships, the Barstow and the Cauldrew and measures the angle between them at be 45°. They radio the Barstow and by comparing known landmarks, the distance between the
The Admiral and the Barstow is found to be 323 meters. The Barstow reports an angle of 59° between the
Admiral and the Cauldrew. To the nearest meter, what is the distance between the Barstow and the Cauldrew?

A) 81 m
B) 235 m
C) 49 m
D) 266 m

Question 51

Choose the one alternative that best completes the statement or answers the question.
Solve the triangle.

Question 52

Solve the problem.

Question 53

Choose the one alternative that best completes the statement or answers the question.
It is 4.7 km from Lighthouse A to Port B. The bearing of the port from the lighthouse is N73°E. A ship has sailed due west from the port and its bearing from the lighthouse is N31°E. How far has the ship sailed from the port?
Round your answer to the nearest 0.1 km.

A) 3.5 km
B) 3.7 km
C) 3.1 km
D) 2.7 km

Question 54

Choose the one alternative that best completes the statement or answers the question.
Solve the triangle.

Question 55

Solve the problem.

Question 56

Choose the one alternative that best completes the statement or answers the question.
Solve the triangle.

Question 57

Solve the problem.
A guy wire to the top of a tower makes an angle of 64° with the level ground. At a point 26 feet farther from the base of the tower and in line with the base of the wire, the angle of elevation to the top of the tower is . What is the length of the guy wire?

A) 38.83 ft
B) 13.13 ft
C) 51.47 ft
D) 19.61 ft

Question 58

Two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no
triangle at all. Solve any triangle(s) that results.

Question 59

Choose the one alternative that best completes the statement or answers the question.
A flagpole is perpendicular to the horizontal but is on a slope that rises 10° from the horizontal. The pole casts a 43-foot shadow down the slope and angle of elevation of the sun measured from the slope is 36°. How tall is the
Pole? Round your answer to the nearest 0.1 foot.

A) 33.5 ft
B) 36.4 ft
C) 35.4 ft
D) 36.2 ft

Question 60

Choose the one alternative that best completes the statement or answers the question.
Solve the triangle.

Question 61

Solve the problem.
The distance from home plate to dead center field in a certain baseball stadium is 402 feet. A baseball diamond is a square with a distance from home plate to first base of 90 feet. How far is it from first base to dead center
Field?

A) 344.3 ft
B) 470 ft
C) 379.6 ft
D) 327.2 ft

Question 62

Solve the triangle. Find the angles  and  first.

Question 63

Solve the problem.

Question 64

Solve the problem.

Question 65

Solve the problem.
A plane takes off from an airport on the bearing S29°W. It continues for 20 minutes then changes to bearing S52°W and flies for 2 hours 20 minutes on this course then lands at a second airport. If the plane' s speed is 420
Mph, how far from the first airport is the second airport? Round your answer correct to the nearest mile.

A) 1011 mi
B) 1111 mi
C) 1110 mi
D) 1010 mi

Question 66

Solve the triangle. Find the angles  and  first.

Question 67

Solve the problem.
A famous golfer tees off on a long, straight 471 yard par 4 and slices his drive 18° to the right of the line from tee to the hole. If the drive went 290 yards, how many yards will the golfer's second shot have to be to reach the
Hole?

A) 752.2 yd
B) 214.8 yd
C) 660.2 yd
D) 419.6 yd

Question 68

Solve the problem.
In flying the 81 miles from Champaign to Peoria, a student pilot sets a heading that is 9° off course and maintains an average speed of 96 miles per hour. After 15 minutes, the instructor notices the course error and
Tells the student to correct his heading. Through what angle will the plane move to correct the heading and how
Many miles away is Peoria when the plane turns?

Question 69

Find the area of the triangle. If necessary, round the answer to two decimal places.

Question 70

Solve the triangle. Find the angles  and  first.

Question 71

Solve the triangle. Find the angles  and  first.

Question 72

Find the area of the triangle. If necessary, round the answer to two decimal places.

Question 73

Find the area of the triangle. If necessary, round the answer to two decimal places.

Question 74

Find the area of the triangle. If necessary, round the answer to two decimal places.

Question 75

Solve the problem.
Island A is 150 miles from island B. A ship captain travels 250 miles from island A and then finds that he is off course and 160 miles from island B. What angle, in degrees, must he turn through to head straight for island B?
Round the answer to two decimal places. (Hint: Be careful to properly identify which angle is the turning
Angle.)

Question 76

Solve the problem.
A ladder leans against a building that has a wall slanting away from the ladder at an angle of 96° with the ground. If the bottom of the ladder is 23 feet from the base of the wall and it reaches a point 52 feet up the wall,
How tall is the ladder to the nearest foot?

A) 61 ft
B) 60 ft
C) 59 ft
D) 58 ft

Question 77

Find the area of the triangle. If necessary, round the answer to two decimal places.

Question 78

Write the word or phrase that best completes each statement or answers the question.
Solve the problem.

Question 79

Solve the problem.
A famous golfer tees off on a straight 390 yard par 4 and slices his drive to the right. The drive goes 280 yards from the tee. Using a 7-iron on his second shot, he hits the ball 180 yards and it lands inches from the hole. How
Many degrees (to the nearest degree) to the right of the line from the tee to the hole did he slice his drive?

Question 80

Find the area of the triangle. If necessary, round the answer to two decimal places.