Question

A man on the top of a bamboo pole observes that the angle of depression of the base and the top of another pole are ${60}^o$ and ${30}^o$ respectively. If the second pole stands $5$ m above the ground level, then the height of the bamboo pole on which the man is sitting is

• A. $5$ m
• B. $2.5$ m
• C. $10$ m
• D. $12.5$ m

Answer 1

The correct option is B $2.5$ m

In $△ABC,\frac{x}{b}=\tan {30}^o\Rightarrow b=x\sqrt{3}$
In $△ADE$
$\frac{x+5}{b}=\tan {60}^o\Rightarrow \frac{x+5}{\sqrt{3}}=b$
Equating we get, $3x=x+5\Rightarrow x=\frac{5}{2}$
$\therefore$ height$=2.5cm$