Question

Find the measure of a central angle that intercepts an arc of 27 inches in a circle whose radius is 10 inches.

Answer 1

154.7°

Explanation:

Formula for calculating length of an arc = theta/360× 2πr

Where r is the radius

theta is the angle subtended by the arc

Given length of an arc = 27in

Radius of the circle = 10in

Substituting this values in the formula to get theta

27 = theta/360 × 2π(10)

27 = theta/360×20π

20π × theta = 360×27

62.832 × theta = 9720

theta = 9720/62.832

theta = 154.7°

Answer 2

S = Rθ

S = 27
R = 10
θ = ?

Since S = Rθ
θ = S/R
= 27/10
= 2.7 radians

To convert 2.7 radians to degrees
2.7×180°/π = 154.69860469°