What is the length of an arc that subtends a central angle of 75 degrees in a circle whose radius is 5 inches?
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!
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.
To find the length of an arc, you can use the formula:
Length of arc = (θ/360) * 2πr
where θ is the central angle in degrees, r is the radius of the circle, and 2π is approximately equal to 6.28.
In this case, the central angle is 75 degrees and the radius is 5 inches. Plugging these values into the formula:
Length of arc = (75/360) * 2π * 5
Simplifying:
Length of arc = (0.2083) * (6.28) * 5
Length of arc ≈ 1.309 inches
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 1.309 inches.
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.