Question

Read the problem carefully. Show your mathematical thinking and record your final solution. A Forest ranger in a 90-foot observation tower sees a fire. The angle of depression to the fire is 7 degree. A. What is the horizontal distance between the tower and the fire? Round to the nearest foot.

Answer 1

For a problem of this nature, we need to assume that the base of the observation tower is at the same elevation as the fire. The tangent of the angle is the ratio of tower height to horizontal distance:
  tan(α) = (tower height)/(horizontal distance)
Rearranging this equation, we have
  (horizontal distance) = (tower height)/tan(α)
Putting in the given values gives
  (horizontal distance) = (90 ft)/tan(7°) ≈ 733 ft