Amap shows the distance between the corner of cactus road and 1st street and the corner of 1st street and merle road as 3 inches. if the scale is 1 in. : 3.7 mi, what is the actual distance?

You have to use the proportion: 1 inch map / 3.7 miles actual distance

Then, 3 inches measured in the map = 3 inch map * 3.7 miles actual distance / 1 inch map = 11.1 miles

11.1 miles

Answer: 10pi

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.

I’m not sure i’m sorry