Question

The angle of depression from a water tower to a forest fire underneath the tower is 18°. If the height of the water tower is 60 meters, what is the horizontal distance on the ground between the water tower and the fire? Round your answer to the nearest meter.

Answer 1

185 m

Explanation:

• The angle of depression from the water tower to a forest fire = 18°

,

• The height of the water tower = 60 meters

We want to find the horizontal distance on the ground between the water tower and the fire.

Let the distance = y

The diagram below illustrates the given information:

We then solve for y.

Using trigonometric ratios:

`\begin{gathered} \tan18=(60)/(y) \\ \text{ Cross multiply} \\ y*\tan18=60 \\ \text{ Divide both sides by }tan\;18 \\ y=(60)/(\tan18) \\ y=184.66 \\ y\approx185\text{ meters} \end{gathered}`

The horizontal distance on the ground between the water tower and the fire is 185 meters (rounded to the nearest meter).