Question

You are standing 164 feet away from the base of a building and your clinometer measures21° when it's looking at the top of the building. (This angle is the one between the groundand the top of the building). Please calculate the height of the building.

Answer 1

Given:

Distance between the person and building is 164 ft.

The angle measures from the ground to the top of a building 21 degrees.

To find the height of the building:

Here, Opposite side is the height of the building

The adjacent side is the horizontal distance.

Using the trigonometry ratio,

$\begin{gathered} \tan \theta=\frac{Opp}{\text{Adj}} \\ \tan 21^{\circ}=\frac{h}{164} \\ h=164\tan 21^{\circ} \\ h=62.9537 \\ h\approx62.95\text{ ft} \end{gathered}$

Hence, the height of the building is, 62.95 ft.