Question

Find the measure of CD. Round to the nearest tenth. PLEASE NEED HELP!!!

Answer 1

Answer:

89.0°

Step-by-step explanation:

The measure of arc CD is the same degree measure as the central angle.

To find the central angle use the right triangle.

The segment from the centre to the chord is a perpendicular bisector, thus

the third side of the triangle = 12.7 ÷ 2 = 6.35

Calculate one half of the central angle using the sine ratio and multiply by 2 for the whole central angle

sin( one- half ) =$\frac{opposite}{hypotenuse}$ = $\frac{6.35}{9.06}$, hence

central angle = 2 × $sin^{-1}$ ($\frac{6.35}{9.06}$ ) ≈ 89.0°

Hence measure of CD ≈ 89.0°