From the top of a tower 100 m high, a man observes two cars on the opposite sides of the tower with angles of…
CBSE Class 10 Maths PYQ · Applications of Trig · Double Triangle · 5 Marks · March 2023 · Standard
Solve it yourself first — then press ↓ or tap Show Solution. Use ←→ for previous / next question.
415 Marks · March 2023 · Standard
From the top of a tower $100 \text{ m}$ high, a man observes two cars on the opposite sides of the tower with angles of depression $30^\circ$ and $45^\circ$ respectively. Find the distance between the two cars. (Use $\sqrt{3} = 1.73$)
Show SolutionHide Solution↓
1 for correct figure $AB = \text{Height of tower} = 100 \text{ m}$ $P$ and $Q$ are position of cars $\angle XBP = \angle APB = 30^\circ$ $\angle YBQ = \angle AQB = 45^\circ$ In $\triangle ABQ$, $\tan 45^\circ = \frac{AB}{AQ} \Rightarrow 1 = \frac{100}{x}$ $\Rightarrow x = 100$ In $\triangle ABP$, $\tan 30^\circ = \frac{AB}{AP} = \frac{100}{y}$ $\frac{1}{\sqrt{3}} = \frac{100}{y} \Rightarrow y = 100\sqrt{3}$ $= 100(1.73) = 173$ Distance between cars = $x + y = 100 + 173 = 273$ $\therefore \text{Distance between cars is } 273 \text{ m}$.
_a_1.png)