Question

1. From the window of one building, the angle of elevation to the top of a second building

is 41° and the angle of depression to the bottom is 54°. The buildings are 56 m apart.
a. How tall is the second building?
b. How high up is the window?

Answer 1

a) the second building is 118.69 m tall

b) the height of the window from the ground is 70.077 m

Explanation:

Attached is a sketch of the building. Look over the sketch before reading the explanation.

Use SOH CAH TOA.

Let
`O_(1)` be the height of the window from the ground.

Therefore we can say that
`O_(1)+O_(2)` is the height of the second building.

We can say that

`O_(1)=tan(x_(1) )*A_(1)`

Therefore

`O_(1)=tan(54)*56`

`O_(1)=70.077`

`O_(2)=tan(x_(2) )*A_(2)`

`O_(2)=tan(41)*56`

`O_(2) =48.68`

`70.007+48.68=118.69`