Question

In a circle with radius 5.1, an angle intercepts an arc of length 30.3. Find the angle in

radians to the nearest 10th.

Answer 1

5.9 radian

Explanation:

Applying,

S = 2πrФ/360°................. Equation 1

Where s = length of the arc, r = radius, Ф = angle.

make Ф the subject of the equation

Ф = 360S/(2πr)........... Equation 2

From the question,

Given: S = 30.3, r = 5.1

Constant: π = 3.14

Substitute into equation 2

Ф = (360×30.3)/(2×5.1×3.14)

Ф = 340.58°

Ф = (340.58×2×3.14)/360

Ф = 5.9 radian