Question

An arc of length 8 in. is intersected by a central angle in a circle with a radius of 3 in. What is the measure of the angle? Round your answer to the nearest tenth. 0.4 radian 1.0 radian 2.7 radians 5.0 radians

Answer 1

2.7 radians

Explanation:

you must convert it + i got it right

Answer 2

The ratio of the measure of the arc length and the circumference is proportional to the measure of the intercepted angle and one whole revolution. If we let x be the measure of the intercepted angle in degrees, the equation will become,

x/360 = 8 in/(2π(3 in))

The value of x from the equation when π = 22/7 is 152.72°.

To convert this value to radians, we use the dimensional analysis as shown below,
in radians = (152.72°)(2π/360°)
in radians = 2.7 radians

Thus, the answer is third choice.