
From the top of a cliff 25 m high the angle of elevation of a tower is found to be equal to the angle of depression of the foot of the tower. The height of the tower is
A. 25 m B. 50 m C. 75 m D. 100 m Answer: Option BShow Answer
Solution(By Apex Team)
Let AB be the tower and CD be cliff Angle of elevation of A is equal to the angle of depression of B at C
Let angle be Q and CD = 25 m
$\begin{array}{l}\text{Let AB}=h\\
\text{CE }\parallel\ \text{DB}\\
\therefore\text{CE}=\text{BD}=x\ \text{(consider)}\\
\text{BE}=\text{CD}=25\ m\\
\therefore\text{AE}=h-25\\
\text{Now in right}\triangle\text{BDC,}\\
\text{tan}\theta=\frac{CD}{BD}=\frac{25}{x}……\left(i\right)\\
\text{and in right }\triangle\text{CAE}\\
\text{tan}\theta=\frac{AE}{CE}=\frac{\left(h-25\right)}{x}……\left(ii\right)\\
\text{From (i) and (ii)}\\
\frac{25}{x}=\frac{h-25}{x}\\
\Rightarrow25=h-25\\
\Rightarrow h=25+25=50\\
\therefore\text{Height of tower}=50\ \text{m}\end{array}$
