Consider circle C below, where the central angle is measured in radians. Circle C is shown. Line segments R C and S C are radii. Angle R C S is StartFraction 5 pi Over 6 EndFraction. Arc R S has a measure of 10 pi. What is the length of the radius?
Answers
Given:
Consider circle C below, where the central angle is measured in radians. Circle C is shown. Line segments R C and S C are radii. Angle R C S is StartFraction 5 pi Over 6 EndFraction. Arc R S has a measure of 10 pi.
To find:
What is the length of the radius?
Solution:
From given, we have,
The central angle is 5π/6.
Arc R S has a measure of 10 pi.
An entire circle is 2π radians, so the part of the circle covered by the angle is given by,
= (5π/6)/2π
= 5/12
The angle 5π/6 represents 5/12th part of the circle.
The sector has a length of 10π units.
The circumference of the circle is given by, 2πr
So, we have,
10π = 5/12 (2πr)
12 × 10π = 5 (2πr)
12 × 10π = 5 × 2 πr
12 × 10π = 10πr
12 = r
Therefore, the length of the radius is 12 units.
Answer:
12 units
Step-by-step explanation:
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