Question

How tall is the building? Explain and show your reasoning. (round to the whole number)

Answer 1

Let h be the height of the building.

For the angle 73º in a right triangle you have the next trigonometric ratio that involves the side h and the distance between you and the bottom of the building:

$\begin{gathered} \tan 73º=\frac{opposite\text{ side}}{Adjacent\text{ side}} \\ \\ \tan 73º=\frac{h}{250} \end{gathered}$

Use the equation above to solve h:

$\begin{gathered} \text{Multiply both sides of the equation by 250:} \\ 250\cdot\tan 73º=250\cdot\frac{h}{250} \\ \\ 250\cdot\tan 73º=h \\ \\ h=250\cdot\tan 73º \\ \\ h=818 \end{gathered}$

Then, the height of the building is 818 meters