Given a circle with the radius of 2, which is the degree measure of an arc whose length is 1/2 pi?
arc-length = rß where ß is in radians
pi/2 = 2ß
ß= pi/4 radians, which is 45 degrees
or
the whole circumference would be 2(pi)r
= 4pi
now by a simple ratio ....
(1/2)pi/(4pi) = angle/360
4angle = 180
angle = 45
To find the degree measure of an arc whose length is given as 1/2 pi in a circle with a radius of 2, you can follow these steps:
1. Recall that the formula to find the length of an arc in a circle is given by:
arc length = (angle measure / 360) * (2 * pi * radius)
2. Rearrange the formula to solve for the angle measure:
angle measure = (arc length / (2 * pi * radius)) * 360
3. Substitute the given values into the formula:
angle measure = (1/2 pi / (2 * pi * 2)) * 360
4. Simplify the expression:
angle measure = (1/4 * 360) = 90 degrees
Therefore, the degree measure of the arc whose length is 1/2 pi in a circle with a radius of 2 is 90 degrees.