Question

If the angle of elevation of a cloud from a point 100 m above a lake is 30° and the angle of depression of the reflection of the cloud in the lake from the same point is 60°, then the height of the cloud above the lake is

• A. 100 m
• B. 150 m
• C. 200 m
• D. 250 m

Answer 1

The correct option is C 200 m

Let the line ON be the lake, C be the cloud and R be the reflection of the cloud in the lake.
Let CM be h.

$In\Delta CML,$
$\tan {30}^{\circ }=\frac{CM}{LM}$
$\Rightarrow \frac{1}{\sqrt{3}}=\frac{h}{LM}$
$\Rightarrow LM=\sqrt{3}h$ ....(i)
Now, $in\Delta LMR,$
$\tan {60}^{\circ }=\frac{RM}{LM}$
$\Rightarrow \sqrt{3}=\frac{RM}{\sqrt{3}h}$ [From (i)]
$\Rightarrow {\left(\sqrt{3}\right)}^{2}h=(h+100)+100$ $(\because RM=RN+MN$
$\text{and}RN=CN=h+100)$
$\Rightarrow 3h=h+200$
$\Rightarrow 2h=200$
$\Rightarrow h=100m$
Thus, the height of the cloud above the lake is (h + 100) = 200 m.
Hence, the correct answer is option (c).