Question

Ms. M was in New York and she wanted to estimate the height of the One World Trade Center building. She has an app on her phone that will measure an angle of elevation. Knowing that there are about 315 feet in a city block, she estimated she was about 825 feet away from the base of the building. She held her phone (with the app) at eye level (about 5 feet off the ground) and measured the angle of elevation to the top of the building to be 65°. What is the height of the building to the nearest foot?

Answer 1

We can draw the following picture

Since we have a right triangle, we can apply the trigonometric functions. For instace,

$\tan 65=\frac{h}{825}$

where h is the height of the building. If we move 825 to the left hand side, we have

$825\cdot\tan 65=h$

so, we obtain

$\begin{gathered} h=825\cdot(2.144) \\ h=1769.22 \end{gathered}$

However, we must add 5 ft to this value in order to obtain the real height of the building, that is

$1769.22+5=1774.22$

so, the answer is 1774.22 ft