Question

A forest ranger in a 110 ft observation tower sees a fire. The angle of depression is 12 degrees. To the nearest foot, what is the distance from the tower to the fire?

Answer 1

The distance from the tower to the fire is 529.10feet

Angle of depression

The distance from the tower to the fire is the hypotenuse of the resulting triangle

Given the following

• Height of the tower = 110ft

Using the SOH CAH TOA identity

sin theta = opp/hyp

sin 12 = 110/H

H = 110/sin12

H = 110/0.2079

H = 529.10

Hence the distance from the tower to the fire is 529.10feet

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