Question

Hey! I need help solvingThis is from my ACT prep guide

Answer 1

Answer:

316.1 ft

Explanation:

Let's sketch the diagram as seen below;

From the above diagram, we can go ahead and determine the length of the opposite side(x) to angle 56 degrees in the upper triangle as seen below;

$\begin{gathered} \tan 56=\frac{x}{150} \\ x=150\cdot\tan 56x \\ x=222.4ft \end{gathered}$

We can also go ahead and determine the length of the opposite side(y) to angle 32 degrees in the lower triangle as seen below;

$\begin{gathered} \tan 32=\frac{y}{150} \\ y=150\cdot\tan 32 \\ y=93.7ft \end{gathered}$

Therefore, the height(h) of the building will be;

$\begin{gathered} h=x+y \\ =222.4+93.7 \\ =316.1ft \end{gathered}$

So the neighboring building is 316.1 ft tall.