A forest ranger is on a 90-foot fire watch tower. He spots a fire at an angle of depression to the fire that is 7 degrees. What is the horizontal distance between the tower and the fire

the horizontal distance between the tower and the fire is 732.89 feet

Step-by-step explanation:

Considering the situation, a right angle triangle is formed. The height of the fire watch tower represents the opposite side of the right angle triangle.

The horizontal distance, h between the tower and the fire represents the adjacent side of the right angle triangle.

If the angle of depression to the fire that is 7°, the angle of elevation from of the tower watcher from the fire is also 7° because they are alternate angles.

To determine h, we would apply

the tangent trigonometric ratio.

Tan θ, = opposite side/adjacent side. Therefore,

Tan 7 = 90/h

h = 90/tan7 = 90/0.1228

h = 732.89 feet

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