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Question

Find PQ, if AB = 150 m, $∠ P = 30^{\circ} a n d ∠ Q = 45^{\circ}$

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Solution

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In $△ A P B$ ,
$tan 30 = \frac{A B}{P B}$
$P B = 150 \sqrt{3}$
In $△ A Q B$
$tan 45 = \frac{A B}{B Q}$
$1 = \frac{150}{B Q}$
$B Q = 150$
Thus, $P Q = P B - B Q$
$P Q = 150 \sqrt{3} - 150$
$P Q = 109.8$

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