Question

A highway curve, in the shape of an arc of a circle is.25 miles. The

direction of the highway changes 45 degrees from one end of the curve
to the other. Find the radius of the circle in feet that the curve follows.
Round your answer to three decimal places.

Answer 1

31.83 miles

Explanation:

1: Find the equation: arc length = 2πr(
`(x)/(360)`)

2: Substitute in your values: 25 = 2πr(
`(45)/(360)`)

3: divide by
`(45)/(360)` on both sides: 2πr =
`(25)/((45)/(360) )` = 200

4: divide by 2 on both sides: πr = 100

5: divide by pi on both sides: r= 31.83 miles