Trigonometrical Ratios And Identities Ques 7
- If the angle of elevation of a cloud from a point $P$ which is $25 \mathrm{m}$ above a lake be $30^{\circ}$ and the angle of depression of reflection of the cloud in the lake from $P$ be $60^{\circ}$, then the height of the cloud (in meters) from the surface of the lake is
(2019 Main, 12 Jan II)
(a) $50$
(b) $60$
(c) $45$
(d) $42$
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Answer:
Correct Answer: 7.(a)
Solution: (a) According to given information, we have the following figure,
In $\triangle P Q M, \tan 30^{\circ}=\frac{x}{y}$ $\quad$ ……..(i)
In $\triangle P R M, \tan 60^{\circ}=\frac{25+(25+x)}{y}$ $\quad$ ……..(ii)
On eliminating ’ $y$ ’ from Eqs. (i) and (ii),
we get
$ \begin{aligned} & \sqrt{3}=\frac{25+(25+x)}{\sqrt{3} x} \\ \Rightarrow \quad & 3 x=50+x \\ \Rightarrow \quad & 2 x=50 \Rightarrow x=25 \mathrm{m} . \end{aligned} $
$\therefore \quad$ Height of cloud from surface
$ =\quad x+25=50 \mathrm{m} \text {. } $
BETA
