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.
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.
