Two pillars of equal lengths stand on either side of a road which is 100 m wide, exactly opposite to each other. At a…
CBSE Class 10 Maths PYQ · Applications of Trig · Double Triangle · 5 Marks · March 2024 · Standard
Solve it yourself first — then press ↓ or tap Show Solution. Use ←→ for previous / next question.
555 Marks · March 2024 · Standard
Two pillars of equal lengths stand on either side of a road which is $100$ m wide, exactly opposite to each other. At a point on the road between the pillars, the angles of elevation of the tops of the pillars are $60^\circ$ and $30^\circ$. Find the length of each pillar and distance of the point on the road from the pillars. (Use $\sqrt{3} = 1.732$)
Show SolutionHide Solution↓
Correct figure Let $AB$ and $CD$ are two pillars of equal length $h$ m and let $P$ be the point on road $x$ m away from pillar $CD$. In $$\begin{aligned}& \triangle CDP \\ & \tan 60^\circ = \sqrt{3} = \frac{h}{x} \\ & \Rightarrow h = \sqrt{3} x ------(i) \\ & \text{In } \triangle ABP, \\ & \tan 30^\circ = \frac{1}{\sqrt{3}} = \frac{h}{100-x} \\ & \Rightarrow h = \frac{100-x}{\sqrt{3}} -------(ii) \\ & \text{Solving eq.(i) and eq.(ii)} \\ & x = 25 \\ & \text{and } h = 25\sqrt{3} = 25 \times 1.732 = 43.3 \\ & \text{The length of each pillar is } 43.3 \text{ m and the distance of the point on the road from pillars is } 75 \text{ m and } 25 \text{ m respectively.}\end{aligned}$$
