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Answer :
This question is incomplete
Complete Question
If the measurement of a central angle is 5pi/6, find the length of its intercepted arc in a circle with a radius of 15 inches
a 33.4 inches
b. 35.6 inches
C. 37.5 inches
d. 39.3 inches
Answer:
d. 39.3 inches
Step-by-step explanation:
We are to find the Arc length of the circle
To solve the above question, the formula is given as:
Arc length = Central angle × radius
From the above Question, we are given:
Central angle = 5pi/6 = 5π/6
Radius = 15 inches
Hence,
Arc length = 5π/6 × 15 inches
Arc length = 235.61944901923448/ 6
Arc length = 39.26990817 inches
Approximately , the Arc length
= 39.3 inches.
Therefore, Option d is the correct answer.
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The length of the intercepted arc is approximately 39.3 inches. Therefore, the correct answer is option D.
To find the length of the intercepted arc when the central angle is [tex]\frac{5\pi}{6}[/tex] radians in a circle with a radius of 15 inches, we use the formula for arc length :
- Arc Length = θ × r
- θ = [tex]\frac{5\pi}{6}[/tex] radians
- r = 15 inches
- Substitute the given values into the formula :
Arc Length = [tex]\frac{5\pi}{6}[/tex] × 15 = [tex]\frac{75\pi}{6}[/tex] = 12.5[tex]\pi[/tex] = 12.5 × 3.14 ≈ 39.3 inches
- Therefore, the length of the intercepted arc is approximately 39.3 inches.
Complete Question :
If the measurement of a central angle is [tex]\frac{5\pi}{6}[/tex] radians, find the length of its intercepted arc in a circle with a radius of 15 inches.
