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?

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)