An arc of length 30 meters is formed by a central angle A on a circle of radius 15. The measure of A in degrees (to two decimal places) is (Points : 5)
0.50
28.65
114.59
0.01
arclength = rØ, where r is the radius, and Ø is the central angle in radians
30 = 15Ø
Ø = 30/15 or 2 radians
π radians = 180°
so 2 radians = 2(180/π)° = appr 114.59°
To find the measure of angle A in degrees, we can use the formula:
Arc Length = Radius * Central Angle
Given that the arc length is 30 meters and the radius is 15, we can rearrange the formula to solve for the central angle:
Central Angle = Arc Length / Radius
Plugging in the given values:
Central Angle = 30 / 15 = 2
Now, to convert the central angle from radians to degrees, we use the conversion factor:
1 radian = 180 degrees / π
Central Angle in degrees = Central Angle in radians * 180 degrees / π
Central Angle in degrees = 2 * 180 degrees / π
Central Angle in degrees ≈ 114.59 degrees
Therefore, the measure of angle A in degrees is approximately 114.59 degrees.
To find the measure of angle A in degrees, we can use the formula:
arc length = radius * central angle in radians
First, let's convert the given arc length from meters to the unit of the radius. Since the radius is given in meters, we need to convert the arc length to radians.
To do this, we will use the formula:
arc length in radians = (arc length in meters) / (radius)
arc length in radians = 30 / 15 = 2 radians
Now, we can use the formula to find the measure of angle A:
arc length = radius * central angle in radians
2 = 15 * central angle in radians
central angle in radians = 2 / 15
To convert the central angle from radians to degrees, we use the formula:
central angle in degrees = (central angle in radians) * (180 / pi)
central angle in degrees = (2 / 15) * (180 / pi)
central angle in degrees ≈ 22.91 degrees (rounded to two decimal places)
Therefore, the measure of angle A in degrees is approximately 22.91 degrees.
Since none of the provided options match this result, none of the given options is the correct answer.