Question

Two posts are $20$ metre apart and the height of one post is double that of the other. From the mid-point of the line segment joining their feet, an observer finds that the angular elevation of their tops are complementary. Then the height of the shorter post (in metre) is

• A. $5\sqrt{2}$
• B. $5$
• C. $20\sqrt{3}$
• D. $10$

Answer 1

The correct option is A $5\sqrt{2}$


Given $\alpha +\beta =\frac{\pi }{2}$
$\tan \alpha =\frac{2h}{10}\tan \beta =\frac{h}{10}\Rightarrow \tan (\frac{\pi }{2}-\alpha )=\frac{h}{10}\Rightarrow \cot \alpha =\frac{h}{10}=\frac{10}{2h}\Rightarrow 2h^2=100\therefore h=5\sqrt{2}m$