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A circle has a radius of 11 ft. Find the radian measure of the central angle A degrees that intercepts an arc of length 5 ft. Do not round any intermediate computations, and round your answer to the nearest tenth.

User Deowk
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1 Answer

5 votes

Answer:

The answer is
(5)/(11)\\ = 0.45; rounded up(to the nearest tenth) is 0.5

Explanation:

The angle measure of a circle in radians is 2
\pi.

First, find the circumference of the circle in terms of
\pi.

The formula for the circumference of a circle is 2
\pir (2 ×
\pi × radius)

Then find the ratio of the arc length of the central angle to the circumference.

Arc length of the central angle = 5.

Circumference = 22
\pi

The ratio of the arc length of the central angle to the circumference is equal to
(5)/(22\pi )

Now use that ratio to find the central angle in radians by multiplying it by the angle measure of the circle in radians.


(5)/(22\pi ) × 2
\pi = 5/11

Round to the nearest tenth:


(5)/(11) ≈ 0.4545 = 0.5

User Jling
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