Question

a circle is drawn centered at an angle's vertex. the circle's radius is 6 cm long and the angle subtends an arc that is 9 cm long. what is the angle's measure in radians?

Answer 1

The measure of the angle in radians is found by dividing the arc length by the radius of the circle. Given an arc length of 9 cm and a radius of 6 cm, the angle measures 1.5 radians.

Step-by-step explanation:

The student is asking how to find the measure of an angle in radians when given the arc length and the radius of a circle. The relationship between the arc length (As), radius (r), and angle in radians (A) is A = As / r.

In this case, the arc length is given as 9 cm, and the radius is 6 cm, so we can find the angle's measure in radians by dividing the arc length by the radius.

The calculation is as follows: A = As / r

= 9 cm / 6 cm

= 1.5 radians.