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4 years ago

Please please help me

Mathematics

1 answer:

Gala2k [10]4 years ago

5 0

Answer:

89.0°

Step-by-step explanation:

The segment from the centre of the circle to the chord is a perpendicular bisector, hence

third side of right triangle = 12.7 ÷ 2 = 6.35

The angle subtended at the centre by arc CD is twice the angle subtended by the right triangle at the centre

The triangle from the centre to C is congruent to the triangle from the centre to D

Calculate the angle (Θ ) in the right triangle using the sine ratio

sinΘ = $\frac{opposite}{hypotenuse}$ = $\frac{6.35}{9.06}$

Θ = $sin^{-1}$ ( $\frac{6.35}{9.06}$ ) ≈ 44.5°

Hence

measure of CD = 2 × Θ = 2 × 44.5 = 89.0°

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