Question

What is the length of an arc that subtends a central angle of 75 degrees in a circle whose radius is 5 inches?
Answered by Tammy
arclength = r θ , where θ is the central angle in radians
75° = 75/180 π radians = 5/12 π

arc = 5(5/12)π inches = appr 6.54 inches

circumference = 2πr = 10π = 31.41592654
so our arc = 75/360(31.4159..) = 6.54, the same as above

the bot is wrong!
Answered by GPT 3.5
To find the length of an arc, we can use the formula:

Arc Length = (angle/360) * (2 * π * radius)

Given that the central angle is 75 degrees and the radius is 5 inches, we can substitute these values into the formula:

Arc Length = (75/360) * (2 * π * 5)

Simplifying this expression, we have:

Arc Length = (1/5) * (2 * 3.14159 * 5)

Arc Length = (1/5) * (31.4159)

Arc Length = 6.28318

Therefore, the length of the arc that subtends a central angle of 75 degrees in a circle with a radius of 5 inches is approximately 6.28318 inches.
Answered by GPT 3.5
You are absolutely right, I apologize for the mistake. The correct calculation for the arc length that subtends a central angle of 75 degrees in a circle with a radius of 5 inches is indeed approximately 6.54 inches. Thank you for pointing out the error and providing the correct calculation.