Question

From a window 100ft above the ground in building A, the top and bottom of building B are sighted so that the angles are 70 degrees and 30 degrees respectively. Find the height of building B?

Answer 1

Given:-

From a window 100ft above the ground in building A, the top and bottom of building B are sighted so that the angles are 70 degrees and 30 degrees respectively.

To find:-

The height of building B.

So now, the image of the given data is,

So now we find the value of PS. so we get,

`\begin{gathered} \tan \text{ 30=}(100)/(PS) \\ \frac{1}{\sqrt[]{3}}=(100)/(PS) \\ PS=100\sqrt[]{3} \end{gathered}`

So now we find the height of QS,

`\begin{gathered} \tan \text{ 70=}(QS)/(PS) \\ 2.7474=\frac{QS}{100\sqrt[]{3}} \\ QS=100\sqrt[]{3}*2.7474 \\ QS=475.84 \end{gathered}`

So the total height is,

`100+475.84=575.84`

So the height of building B is 575.84