Question

A pilot is flying over a straight highway. He determines the angles of depression to two mileposts, 15 mi apart, to be 32° and 48°, as shown in the figure. Round youranswers to the nearest tenth mile.

Answer 1

The angles 32 and 48 leave 80 degrees (ie the angle between the two mileposts

To find the distance from plane to 32 milepost
Using Rule of Sines a/sin A = b/Sin B

15/sin80 = c/sin 32

c = sin 58/sin80 *15 = 12.916 miles

To find height (s=o/h) o= sin32*12.916

Opp = 6.844 miles (Height)
Dist from 32 degree milepost to point under plane

tan = o/a

6.844/tan32= 10.95 miles

***************** 80?
*************
*****hyp=12.916 ht(opp)=6.844
*****
32?____________|__________58?_

<----------10.95----->