4-2 Degrees and Radians
Find the length of the intercepted arc with the
given central angle measure in a circle with the
given radius. Round to the nearest tenth.
27. 31. 45°, r = 5 mi
SOLUTION: Method 1 Convert 45° to radian measure, and then use s = rθ
to find the arc length.
, r = 2.5 m
SOLUTION: Substitute r = 5 and θ = 29. .
, r = 4 yd
SOLUTION: Method 2 Use s =
to find the arc length.
31. 45°, r = 5 mi
SOLUTION: Method 1 Convert 45° to radian measure, and then use s = rθ
to find the arc length.
33. AMUSEMENT PARK A carousel at an Substitute r = 5 and θ = .
amusement park rotates 3024° per ride.
a. How far would a rider seated 13 feet from the
center of the carousel travel during the ride?
b. How much farther would a second rider seated 18
feet from the center of the carousel travel during the
ride than the rider in part a?
SOLUTION: a. In this problem, θ = 3024° and r = 13 feet.
Convert 3024º to radian measure.
Method 2 Use s =
to find the arc length.
Substitute r = 13 and θ = 16.8π into the arc length
formula s = rθ.
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b. Let r1 represent the distance the first rider is from
Therefore, the second rider would travel about 264
feet farther than the first rider.
4-2 Degrees and Radians
Find the area of each sector.
33. AMUSEMENT PARK A carousel at an amusement park rotates 3024° per ride.
a. How far would a rider seated 13 feet from the
center of the carousel travel during the ride?
b. How much farther would a second rider seated 18
feet from the center of the carousel travel during the
ride than the rider in part a?
43. SOLUTION: SOLUTION: The measure of the sector’s central angle θ is 102°
and the radius is 1.5 inches. Convert the central
angle measure to radians.
a. In this problem, θ = 3024° and r = 13 feet.
Convert 3024º to radian measure.
Substitute r = 13 and θ = 16.8π into the arc length
formula s = rθ.
Use the central angle and the radius to find the area
of the sector.
b. Let r1 represent the distance the first rider is from
Therefore, the area of the sector is about 2.0 square
inches.
the center of the carousel and r2 represent the
distance the second rider is from the center. For the
second rider, r = 18 feet.
45. Therefore, the second rider would travel about 264
feet farther than the first rider.
SOLUTION: The measure of the sector’s central angle θ is Find the area of each sector.
and the radius is 12 yards.
43. SOLUTION: Therefore, the area of the sector is about 90.5
square yards.
The measure of the sector’s central angle θ is 102°
and the radius is 1.5 inches. Convert the central
angle measure to radians.
UseManual
the central
angle
and the
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of the sector.
radius to find the area
47. Page 2
SOLUTION: The measure of the sector’s central angle θ is 177°
areaRadians
of the sector is about 90.5
4-2 Therefore,
Degreesthe
and
square yards.
Therefore, the area of the sector is about 500.5
square feet.
49. GAMES The dart board shown is divided into twenty equal sectors. If the diameter of the board is
18 inches, what area of the board does each sector
cover?
47. SOLUTION: The measure of the sector’s central angle θ is 177°
and the radius is 18 feet. Convert the central angle
measure to radians.
SOLUTION: Use the central angle and the radius to find the area
of the sector.
360° ÷ 20 or 18°
If the board is divided into 20 equal sectors, then the
central angle of each sector has a measure of 18°. So, the measure of a sector’s central angle is 18°
and the radius is 9 inches.
Convert the central angle measure to radians.
Therefore, the area of the sector is about 500.5
square feet.
49. GAMES The dart board shown is divided into Use the central angle and the radius to find the area
of a sector.
twenty equal sectors. If the diameter of the board is
18 inches, what area of the board does each sector
cover?
Therefore, each sector covers an area of about 12.7
square inches.
SOLUTION: 360° ÷ 20 or 18°
If the board is divided into 20 equal sectors, then the
central angle of each sector has a measure of 18°. So, the measure of a sector’s central angle is 18°
and the radius is 9 inches.
The area of a sector of a circle and the measure
of its central angle are given. Find the radius of
the circle.
51. A = 29 ft2, θ = 68°
SOLUTION: Convert the central angle measure to radians.
Convert the central angle measure to radians.
Substitute the area and the central angle into the
area formula for a sector to find the radius.
Use the central angle and the radius to find the area
of a sector.
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covers an area of about 12.7
4-2 Therefore,
Degreeseach
andsector
Radians
square inches.
The area of a sector of a circle and the measure
of its central angle are given. Find the radius of
the circle.
51. A = 29 ft2, θ = 68°
SOLUTION: Convert the central angle measure to radians.
Substitute the area and the central angle into the
area formula for a sector to find the radius.
Therefore, the radius is 7 ft.
53. A = 377 in2, θ =
SOLUTION: Therefore, the radius is 12 in.
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