A forest ranger is watching the progress of a forest fire sp

A forest ranger is watching the progress of a forest fire spreading towards her from the top of a 3760-foot mountain. In 7 minutes, the angle of depression to the leading edge of the fire changed from 0.67 radians to 1.14 radians. How many feet does the fire advance during the 7 minutes the ranger observed the fire? At what speed (in feet per minute) is the fire spreading towards the ranger? feet per minute

Solution

Angle of Depression = angle of elevation from fire.
tan = H/Distance
D = H/tan
tan(0.67)=0.7923
D = 4745.95 ft

tan(1.14) = 2.175875
D= 3760/2.175875 =1728.04 ft

= 3017.91 ft

Using Unit Cancellation technique:
3017.91ft/7 min = 431.13 ft/min