Question

HeyI need help with this, having trouble solvingIt is from my ACT prep guide

Answer 1

We will determine the height of the building as follows:

First, we determine the height above her window, that is:

`\tan (56)=(h_u)/(150ft)\Rightarrow h_u=(150ft)\tan (56)`
`\Rightarrow h_u=222.3841453\ldots ft`

Now, we calculate the height below her window:

`\tan (32)=(h_l)/(150ft)\Rightarrow h_l=(150ft)\tan (32)`
`\Rightarrow h_l=93.73040279\ldots ft`

Then, we will have that:

`h_T=h_l+h_l\Rightarrow h_T=150(\tan (56)+\tan (32))`
`\Rightarrow h_T=316.1145581\ldots ft\Rightarrow h_T\approx316.1ft`

So, the height of the building is approximately 316.1 ft tall.