Question

you are standing 160 meters away from the base of a building. the angle of elevation to the top of the building is 38 degrees. what is the height of the building? round your answer to 3 decimal places.

Answer 1

Let's draw the situation:

Because the ground and the building make a 90° angle, we have a right triangle. We know one angle and its adjacent leg, and we want the opposite leg. Thus, we can use the tangent of the angle:

`\begin{gathered} \tan 38\degree=(h)/(160) \\ h=160\tan 38\degree\approx160\cdot0.781286\approx125.006 \end{gathered}`

So, the height of the building is approximately 125.006 m.