Question

For a circle with a radius of 6 feet, what is the measurement of the central angle (in degrees) that intercepts an arc with a length of
9π
2
feet?

Answer 1

The measurement of the central angle is 135 degrees

Solution:

The length of arc when angle given in degrees is given as:

$Arc\ length = \frac{ \theta }{360} \times 2 \pi r$

Where,

r is the radius

$\theta$ is the central angle in degrees

From given,

$r = 6\ feet\\\\Arc\ length = \frac{ 9 \pi }{2}\ feet$

Substituting the values we get,

$\frac{9 \pi }{2} = \frac{ \theta }{ 360} \times 2 \times \pi \times 6\\\\9 \times 360= \theta \times 24\\\\\theta = 135$

Thus the measurement of the central angle is 135 degrees