Question

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

Answer 1

1675 feet

Explanation:

Refer to the image attached for diagrams and better explanations

Answer 2

1675 ft

Explanation:

For us to calculate how close the windmill is to the fire, if we imagine it as a triangle, the distance from watch tower to the fire will be:

tan θ= opposite/adjacent

opposite=140 ft

adjacent = x

θ=3°

Thus;

tan 3 = 140/x

x=140/tan 3

x = 2,671.359 ft

Now, 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=996.15 ft

Now, the distance between fire and wind mill will be:

x - y = 2671.359 - 996.15

x - y = 1675.209 ≈ 1675 ft