Question

From the top of $7m$ high building, the angle of elevation of the top of a cable tower is $60°$ and the angle of depression of its foot is $45°$. Determine the height of the tower.

Answer 1

Solve for the height of the tower :

Given,

1. Height of building$=7m$.

2. Angle of elevation of the top of a cable tower$=60°$.

3. Angle of depression to the foot of a cable tower$=45°$.

From the figure,

$$\begin{gathered} \tan \left(45°\right)=\frac{AB}{BC} \\ \Rightarrow 1=\frac{AB}{BC} \\ \Rightarrow AB=BC=7m \\ \tan \left(60°\right)=\frac{ED}{AD} \\ \Rightarrow \sqrt{3}=\frac{ED}{7}[\because AD=BC] \\ \Rightarrow ED=7\sqrt{3}m \end{gathered}$$

Height of tower $=ED+CD$

$=7\sqrt{3}+7\left[\because AB=CD\right]$

$\Rightarrow$Height of tower$=19.12m$

Hence, height of the tower is $19.12m$.