Question

Find the measure of CD.
Round to the nearest tenth.
mCD= [?]

Answer 1

The arc CD would be 114.6°

We use- sin x = opposite / hypotenuse

In the problem the opposite side of angle x = 36.7/2 and the hypotenuse = 21.8

So:

sin x = [36.7/2] / [21.8]

sin x = 18.35 / 21.8

sin x = 0.8417

x = arc sin (0.8417)

x = 57.32°

So the angle formed at the center by CD would have to be 2 x 57.32 = 114.64°

BUT, it says to round to the nearest tenth, so the answer would therefore, the arc CD is: 114.6°

Answer 2

The arc CD is: 114.64°

Explanation:

The given triangle inside the circle, we can get the trigonometric ratio such as

sin x = opposite / hypotenuse

Here:

The opposite side of angle x = 36.7/2

The hypotenuse = 21.8

Thus,

sin x = [36.7/2] / [21.8]

sin x = 18.35 / 21.8

sin x = 0.8417

x = arc sin (0.8417)

x = 57.32°

Thus, the angle formed at the center by CD is:

2 x 57.32 = 114.64°

Therefore, the arc CD is: 114.64°