Question

Need help solving this problem This is from my ACT prep guide

Answer 1

`h=101.7\text{ ft}`

Explanation:

To approach this situation, let's make a diagram of it;

To solve this problem we can use trigonometric relationships since there are right triangles involved; trigonometric relationships are represented as

`\begin{gathered} \sin (\text{angle)}=\frac{\text{opposite}}{\text{ hypotenuse }} \\ \cos (\text{angle)}=\frac{\text{adjacent}}{\text{hypotenuse}} \\ \tan (\text{angle)}=\frac{\text{opposite}}{\text{adjacent}} \end{gathered}`

Then, since we can divide the neighbor building into two parts compounded by two right triangles, use the tan relationship for the 56 degrees triangle, and sin relationship for the 32 degrees triangle:

`\begin{gathered} \tan (56)=\frac{h_1}{150_{}} \\ h_1=150\cdot\tan (56) \\ h_1=22.2\text{ ft} \\ \\ \sin (32)=(h_2)/(150) \\ h_2=150\cdot\sin (32) \\ h_2=79.5\text{ ft} \end{gathered}`

Hence, for the total height of the building:

`\begin{gathered} h=h_1+h_2 \\ h=22.2+79.5 \\ h=101.7\text{ ft} \end{gathered}`