Question

A forest ranger in a 140-foot observation tower sees a fire moving in a direct path toward the windmill by the lake. The angle of depression to the fire is 3°, and the angle of depression to the windmill is 8°. To the nearest foot, how close is the fire to the windmill?

Answer 1

To get how close the windmill is to the fire we proceed as follows:
distance from watch tower to the fire will be:
tan θ= opposite/adjacent
opposite=140 ft
adjacent=x
θ=3°
hence
tan 3=140/x
x=140/tan 3
x=2,671.36 ft

the distance from watch tower to windmill will be:
tan θ=opposite/ adjacent
θ=8°
opposite=140 ft
adjacent=y
thus
tan 8=140/y
y=140/tan8
y=999.15 ft
the distance between fire and wind mill will be:
2,671.36-999.15
=1675.21~1675 ft (to the nearest ft)