Question

From her window, Sandra looks up to the top of a neighboring building at an angle of 36". Her angle of depression to the bottom of the building is 22 The neighboring building is 200 feet away from the building Sandra is in How tall is the neighboring building? Enter your answer, rounded to the nearest tenth of a foot, in the box

Answer 1

ANSWER

The neighboring building is 226.11 feet tall

EXPLANATION

We can start by doing a diagram of this problem:

We want to find x = x1 + x2.

Knowing the angle and one of the sides for each right triangle we can find x1 and x2.

$\begin{gathered} \tan 36º=\frac{x_1}{200} \\ x_1=200\tan 36º \\ x_1=145.31 \end{gathered}$$\begin{gathered} \tan 22º=\frac{x_2}{200} \\ x_2=200\tan 22º \\ x_2=80.8 \end{gathered}$

The height of the neighboring building is:

$x=x_1+x_2=226.11$