Question

for each of the following angles, assume that the terminal ray of the angle opens up in the counter-clockwise direction. a circle with a radius 5 cm long is centered at angle a's vertex, and angle a subtends an arc length of 6 cm along this circle. the subtended arc is how many times as long as the circle's radius?

Answer 1

The subtended arc length of 6 cm is 1.2 times the circle's radius of 5 cm.

Step-by-step explanation:

The student's question is about the relationship between the arc length subtended by an angle and the radius of the circle.

Given that a circle with a radius of 5 cm subtends an arc of 6 cm, the length of the arc is how many times the radius of the circle. The arc length (As) is the length of the part of the circumference that corresponds to the angle that the radius has swept through.

We have been given that the radius (r) is 5 cm, and the arc length (As) is 6 cm.

To find how many times the arc length is as long as the circle's radius, we simply divide the arc length by the radius:

As / r = 6 cm / 5 cm

= 1.2

Hence, the subtended arc is 1.2 times as long as the circle's radius.