JEE Mains · Maths · STD 11 - Trigonometrical equations
If the angle of elevation of a cloud from a point \(P\) which is \(25\,m\) above a lake be \(30^o\) and the angle of depression of reflection of the cloud in the lake from \(P\) be \(60^o,\) then the height of the cloud (in meters) from the surface of the lake is
- A \(60\)
- B \(50\)
- C \(45\)
- D \(42\)
Answer & Solution
Correct Answer
(B) \(50\)
Step-by-step Solution
Detailed explanation
\(\tan \,{30^o}\, = \,\frac{x}{y} \Rightarrow \,y\, = \,\sqrt 3 x\) ....... \((i)\) \(\tan \,{60^0}\, = \frac{{25 + x + 25}}{y}\) \( \Rightarrow \,\sqrt 3 y\, = \,50\, + \,x\) \( \Rightarrow 3x = 50 + x\) \( \Rightarrow x = 25\,m\) \(\therefore \) Height of cloud form surface…
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