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 3780-foot mountain. In 9 minutes, the angle of depression to the leading edge of the fire changed from 0.78 radians to 1.11 radians. How many feet does the advance during the 9 minutes the ranger observed the fire? At what speed (in feet per minute) is the fire spreading towards the ranger?

Solution

Angle of Depression = angle of elevation from fire.
tan = H/Distance
D = H/tan
tan(0.78) = 0.9893
D = 3820.88 ft

tan(1.11) = 2.0143
D= 1876.58

= 1944.3 ft

Using Unit Cancellation technique:
1944.3ft/9min (60min/hr)(1mi/5280ft) = 2.45 mph