OMG Test due in like 15 min! A running track in the shape of an oval is shown. The ends of the track form semicircles.

A running track is shown. The left and right edges of the track are identical curves. The top and bottom edges of the track are straight lines. The track has width 54 m and length of one straight edge 120 m.
What is the perimeter of the inside of the track? (π = 3.14) (1 point)

409.56 m
480.00 m
579.12 m
616.80 m

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

you forgot an image

step-by-step explanation: