A state park is designed in a circular pattern as shown. Martha rides her bike along the circular path from the ranger station to the pool. How far does she ride to the nearest hundredth of a mile?

Question

anonymous · Answer

attachment

anonymous · Answer

answer choices
a).79 miles
b)1.6 miles
c)2.3 miles
d)3.7 miles

bahrom7893 · Answer

what's the formula for the length of an arc?

mertsj · Answer

45 degrees is 1/8 of the circle.  The circle has radius 1 mile so it has circumference 2 pi miles.  1/8 of 2 pi miles is 1/4 pi miles or .79 miles

anonymous · Answer

@bahrom do you mean in general or from the problem?
@Mertsj thanks

mertsj · Answer

yw

bahrom7893 · Answer

in general.. wasn't it something about the angle?

mertsj · Answer

Arc length = r theta but theta must be in radians.

bahrom7893 · Answer

ohh yea.. it's easier to convert though.. i think

mertsj · Answer

Well yes.  45 degrees is pi/4 radians.  pi/4(1)=pi/4.  But he obviously didn't know the formula so he needed to be able to reason it out.

anonymous · Answer

how did you convert 1/4 to .79

mertsj · Answer

I didn't.  I converted 1/4pi to .79 by dividing pi by 4

mertsj · Answer

$$\frac{1}{4}\pi=\frac{\pi}{4}=\frac{3.14159}{4}=.79$$

anonymous · Answer

oh thank you

mertsj · Answer

yw