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Question

Find angle 'x' if :

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Solution

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Let the triangle be ABC, where $∠ A = x$
$B D ⊥ A C$
Now, In $△ B D C$
$tan 60 = \frac{P}{B} = \frac{D C}{B D}$
$B D = \frac{30}{\sqrt{3}}$ = $10 \sqrt{3}$
Now, In $△ A B D$
$sin x = \frac{P}{H} = \frac{B D}{A B}$
$sin x = \frac{10 \sqrt{3}}{20}$
$sin x = \frac{\sqrt{3}}{2}$
$sin x = sin 60$
$x = 60^{\circ}$

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