Question

From the top of a tower, the angles of depression of two objects on the same side of the tower are found to be $\alpha$ and $\beta$ where $\alpha >\beta$.

The height of the tower is $130m,$ $\alpha ={60}^{o}and\beta ={30}^o$.

The distance of the extreme object from the top of the tower is

• A. $65m$
• B. $130m$
• C. $260m$
• D. None of the above

Answer 1

Answer: (C)

$260m$

the extreme object from the top of the tower has low angle of depression

$\therefore$ The angle of elevation of the point = ${30}^{\circ }$

Height of the tower, h= $130$ m

Let the distance of the point from the top of the tower = $p$

Thus, $\sin 30=\frac{h}{p}$

$\frac{1}{2}=\frac{130}{p}$

$p=260$ m