Deck 6: Trigonometric Functions: Right Triangle Approach

Question 1

Find the length of an arc of a circle of radius 4 km if the arc subtends a central angle of radians.

Answer 1

km

Question 2

Find the angle in the figure.
9.5 m
4 m

Answer 2

radians

Question 3

Find the radius of a circle in which a sector with central angle 3 radians has an area of .

Answer 3

, since is positive.

Question 4

Find an angle between and that is coterminal with each angle given.
a. b. c.

Question 5

From the top of a ft lighthouse, the angle of depression to a ship in the ocean is . How far is the ship from the base of the lighthouse?

Question 6

Find the area of a sector with central angle in a circle with radius m.

Question 7

A boy is riding a scooter whose wheels are inches in diameter. If the wheels rotate at rpm, find the speed at which he is traveling in mi/h.

Question 8

How many revolutions will a bicycle wheel of diameter 26 inches make as the bicycle travels a distance of miles?

Question 9

Find the area of a sector with central angle in a circle with radius m.

Question 10

Two cities, and lie on the same meridian, one is found at S and the other at S. Find the distance between these cities given that the circumference of the earth is mi.

Question 11

Two cities in the western hemisphere lie approximately on the same meridian. Guatemala city has latitude of N and Baton Rouge, Louisiana N. Find the distance between these two cities. (The radius of the earth is miles.)

Question 12

Find the length of the arc in the figure.
5 cm
s

Question 13

Find an angle between and that is coterminal with each angle given.
a. b. c.

Question 14

Find the radian measures that correspond to the degree measures and .

Question 15

Find the degree measures that correspond to the radian measures and .

Question 16

Find the length of an arc of a circle of radius m if the arc subtends a central angle of .

Question 17

Find the length of an arc of a circle of radius m if the arc subtends a central angle of .
 

Question 18

Find the radian measures that correspond to the degree measures and .

Question 19

Find the length of an arc of a circle of radius ft if the arc subtends a central angle of .

Question 20

A ft tree casts a shadow that is ft long. What is the angle of elevation of the sun?

Question 21

Find the reference angle for .

Question 22

Find the reference angle for .

Question 23

Find the reference angle for .

Question 24

Find the reference angle for

Question 25

Find the exact value of .

Question 26

Find the exact value of .

Question 27

Find the exact value of .

Question 28

A ft guy wire is attached to the top of a tower. If the wire makes a angle with the ground, how tall is the tower?

Question 29

Solve for correct to one decimal place.

Question 30

A 12-ft ladder leans against a building so that the angle between the ground and the ladder is . How high does the ladder reach on the building?

Question 31

Find the reference angle for

Question 32

A surveyor stands at a point miles away from the base of a radio tower. He measures the angle of elevation to the top of the tower to be . Find the height of the tower to the nearest foot.

Question 33

A ft tree casts a shadow that is ft long. What is the angle of elevation of the sun?

Question 34

To estimate the height of a building above a level plain, a surveyor measures the angle of elevation to the top of the building to be . Three hundred feet closer to the building the angle of elevation is . Estimate the height of the building. Round your answer to the nearest foot.

Question 35

Find the reference angle for

Question 36

A helicopter is dropping water on a forest fire from a height of ft. If one side of the fire makes an angle of depression of , and the other side makes an angle of depression of on the other side of the helicopter, how wide is the fire.

Question 37

A 22-ft ladder leans against a building so that the angle between the ground and the ladder is . How high does the ladder reach on the building?

Question 38

At a point ft from the base of a building, the angles of elevation to the bottom of a radio transmission tower and to the top of the tower are and . Find the height of the radio tower to the nearest foot.

Question 39

A 18-ft ladder leans against a building so that the angle between the ground and the ladder is . How high does the ladder reach on the building?

Question 40

Find the exact value of .

Question 41

Use a calculator to find an approximate value of each expression correct to five decimal places, if it is defined.
(a)

(b)

Question 42

Find the area of the shaded region.

Question 43

Find the values of the trigonometric functions of given that and .

Question 44

Find the quadrant in which lies given that and .

Question 45

Find the exact value of .

Question 46

The time in seconds that it takes for a sled to slide down a hillside inclined at an angle is where d is the length of the slope in feet. Find the time it takes to slide down a 4000-ft slope inclined at

Question 47

Use a calculator to find an approximate value of each expression correct to five decimal places, if it is defined.
(a)

(b)

Question 48

Find the exact value of .

Question 49

Find the area of the shaded region.

Question 50

Find the exact value of each expression, if it is defined.
(a)
(b)
(c)

Question 51

Find the exact value of each expression, if it is defined.
(a)
(b)
(c)

Question 52

Find the exact value of .

Question 53

Find the exact value of each expression, if it is defined.
(a)
(b)
(c)

Question 54

Find the area of a triangle with sides of length 12 and 22 and included angle .

Question 55

Find the exact value of each expression, if it is defined.
(a)
(b)
(c)

Question 56

Find the values of the trigonometric functions of given that and .

Question 57

The time in seconds that it takes for a sled to slide down a hillside inclined at an angle is where d is the length of the slope in feet. Find the time it takes to slide down a 5000-ft slope inclined at

Question 58

Find the area of the triangle.

Question 59

Find the exact value of .

Question 60

Use a calculator to find an approximate value of each expression correct to five decimal places, if it is defined.
(a)

(b)

Question 61

Find the exact value of the expression.

Question 62

Find the exact value of the expression.

Question 63

Find the angle in the triangle.

Question 64

Find all angles between and satisfying the given equation.

Question 65

Find the angle in the triangle.

Question 66

Find all angles between and satisfying the given equation.

Question 67

Find the angle in the triangle.

Question 68

Rewrite the expression as an algebraic expression in x.

Question 69

Find the exact value of the expression.

Question 70

Find all angles between and satisfying the given equation.

Question 71

A 76-ft tree casts a shadow that is 100 ft long. What is the angle of elevation of the sun?

Question 72

Use a calculator to find an approximate value of each expression correct to five decimal places, if it is defined.
(a)

(b)

Question 73

Rewrite the expression as an algebraic expression in x.

Question 74

A 86-ft tree casts a shadow that is 110 ft long. What is the angle of elevation of the sun?

Question 75

Use the Law of Sines to find .

Question 76

Use the Law of Sines to find .

Question 77

Solve the triangle using the Law of Sines.

Question 78

Find all angles between and satisfying the given equation.

Question 79

Find the exact value of the expression.

Question 80

Find the exact value of the expression.