23.

24.

Convert the angle in radians to degrees.

(Simplify your
answer.)

25.

Convert the angle in degrees to radians.

5°

26.

Convert the angle in degrees to radians.

-20°

27.

Convert the angle in degrees to radians.

141°

**radian**(s)

(Simplify your answer. Round to two decimal places as needed.)

28.

Convert the angle in radians to degrees.

3.23

(Round to two decimal
places as needed.)

29.

Convert the angle in radians to degrees.

10

(Simplify your answer. Round to two decimal places as needed.)

30.

(Round to two decimal
places.)

31.

Find the length s of the arc of a circle of radius
centimeters subtended by the central

angle 1/3 radian.

32.

s denotes the length of the arc of a circle of radius r
subtended by the central angle .

Find the missing quantity.

θ =1/2 radian, s = 3 feet, r =?

The radius of the circle is
feet. (Simplify your answer.)

33.

Find the central angle θ which subtends an arc of length
15 miles of a circle of radius

21 miles.

(Round to six decimal
places as needed.)

Convert to degrees.

(Round to three decimal places as
needed.)

34.

Find the length s of the arc of a circle of radius 20
feet subtended by the central angle

78°.

(Round to three
decimal places.)

35.

Find the area A of the sector of a circle of radius 20
miles formed by the central angle

1/10 radian.

(Round to three
decimal places.)

36.

(Round to three
decimal places.)

37.

Find the length s and area A.

(Round to three decimal places as needed.)

(Round to three decimal places as needed.)

38.

Find the length s and area A.

**The length of the arc is
yards.**

(Round to three decimal places as needed.)

**The area A of the sector is square
yards.**

(Round to three decimal places as needed.)

39.

The minute hand of a clock is 5 inches long. How far does
the tip of the minute hand

move in 20 minutes?

inches (Round to
three decimal places.)

40.

A water sprinkler sprays water over a distance of 20 feet

while rotating through an angle of 125°.
What area of lawn

receives water?

The area A of the sector is
square feet.

(Round to two decimal places as needed.)

41.

An object is traveling around a circle with a radius of
10 inches. If in 50 seconds a

central angle of 1/4 radian is swept out, what are the linear and angular
speeds of the

object?

**The linear speed of the object is**

(Round to three decimal places.)

**The angular speed of the object is**

(Round to three decimal places.)

42.

The diameter of each wheel of a bicycle is 28 inches. If
you are traveling at a speed of

15 miles per hour on this bicycle, through how many revolutions per minute
are the

wheels turning?

43.

City A is due north of City B. Find the distance between
City A ( 37°2'
north latitude)

and City B (19°38'
north latitude). As sume that the radius of Earth is 3960 miles.

The distance between City A and City B is
miles.

(Round to the nearest mile as needed.)

44.

A planet rotates on an axis through its poles and 1
revolution takes 1 day (1 day is 26

hours). The distance from the axis to a location on the planet 30°
north latitude is about

2253.5 miles. Therefore, a location on the planet at 30°
north latitude is spinning on a

circle of radius 2253.5 miles. Compute the linear speed on the surface of
the planet at

30°
north latitude.

**The linear speed on the surface of the planet is
miles/hr.**

(Round the final answer to the nearest integer as needed. Round all
intermediate values

to five decimal places as needed.)

45.

To approximate the speed of the current

of a river, a circular p addle wheel with

radius 6 ft. is lowered into the water . If

the current causes the wheel to rotate at a

speed of 20 revolutions per minute, what

is the speed of the current?

**The speed of the current is **

(Round to two decimal places.)

46.

At a museum you can see the four cable lines that are
used to pull cable cars up and

down a hill. Each cable travels at a speed of 9.45 miles per hour, caused by
a rotating

wheel whose diameter is 7.5 feet. How fast is the wheel rotating? Express
your answer

in revolutions per minute.

The angular speed of the wheel is
rev/min.

(Round to two decimal places as needed.)