Question

Find $PQ$, if $AB=150m,\angle P={30}^{\circ }$ and $\angle Q={45}^{\circ }$

Answer 1

In $△APB$,
$\tan 30=\frac{AB}{PB}$
$PB=150\sqrt{3}$
In $△AQB$
$\tan 45=\frac{AB}{BQ}$
$1=\frac{150}{BQ}$
$BQ=150$
Thus, $PQ=PB-BQ$
$PQ=150\sqrt{3}-150$
$PQ=109.8$