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3 years ago

The diagram below shows circle 0 with radii OA and OB. The length of a radius is 6

Mathematics

1 answer:

shepuryov [24]3 years ago

5 0

Answer:

124°

Step-by-step explanation:

We are to solve for the central angle.

In the question,

We are given

The length of the radius or radius = 6 inches

The length of the arc or the arc length (AB) = 13 inches

The formula for the Arc length of a circle = 2πr × (central angle in degree ÷ 360)

From the above formula, we can derive our formula for the measure of the central angle.

The formula for the measure of the central angle AOB =( Arc length × 360 ) ÷ 2πr

Angle AOB = (13 inches × 360) ÷ 2 × π × 6 inches

Angle AOB = 4680 ÷ 37.699111843

Angle AOB = 124.14083392°

Approximately Angle AOB to the nearest degree = 124°

Therefore, the measure of angle AOB to the nearest degree = 124°

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