Question

Circle O shown below has a radius of 29 inches. Find, to the nearest tenth of a degree, the measure of the angle, x, that forms an arc whose length is 55 inchesA. 108.7 degreesB. 154.6 degreesC. 4.4 degreesD. 13.9 degrees

Answer 1

EXPLANATION

Suppose the circle of a circunference is 10 inches. If we have a semicircle, it is literally half of a circle and angle will be equal to 180°. Since it is a half that means the arc of this semicircle is half of the total circunference. So, here we have the portion that represents the arc and what is the total circunference to take that portion of.

In this case, the arc is 55 inches, and the total arc is given by equation:

Total circunference arc = 2πr = 2*π*(29) = 58π ≈ 182.21 inches

what portion of 182 is 55 inches?

Well, 55/182.21 =0.302 * 100= 30.2%

So, 55 inches is 30% of the total arc.

Then, multiplying this fraction by 360 will give us the angle that represents this arc.

360° * 0.302 ≈ 108.7°

Answer is A) 108.7 degrees