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