Question

Find PQ, if AB = 150 m, ∠P = 30° and ∠Q = 45°.

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Answer 1

From ΔAPB

tan 30° = ${\displaystyle \frac{\text{AB}}{\text{PB}}}$

${\displaystyle \frac{1}{\sqrt{3}}=\frac{150}{\text{PB}}}$

PB = ${\displaystyle 150\sqrt{3}}$

PB = 259.80 m

Also, from ΔABQ

tan 45° = ${\displaystyle \frac{\text{AB}}{\text{BQ}}}$

1 = ${\displaystyle \frac{150}{\text{BQ}}}$

BQ = 150 m

Therefore,

PQ = PB - BQ

PQ = 259.80 - 150

PQ = 109.80 m