Question

A wireless pole 25 metres high is fixed on the top of a verandah of a house which is 15 metres high. At a point R on the ground directly opposite the wireless pole and verandah subtend equal angles. Find the distance of R from the verandah.

• A. $30$ m
• B. $15$ m
• C. $25$ m
• D. $40$ m

Answer 1

The correct option is A $30$ m

Let the distance of $R$ from verandah be $x$

Given height of the pole $=25\text{m}$

height of the house $=15\text{m}$

In $△PQR,\tan \theta =\frac{15}{x}$

In $△MPR,\tan 2\theta =\frac{40}{x}$

$⟹\frac{2\tan \theta }{1-{\tan }^2\theta }=\frac{40}{x}$

$⟹\frac{2\times \frac{15}{x}}{1-(\frac{15}{x}{)}^2}=\frac{40}{x}$

$⟹\frac{3x}{x^2-225}=\frac{4}{x}$

$⟹x^2=4\times 225$

$⟹x=30\text{m}$