Question

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

• A. $978.8$
• B. $524.4$
• C. $279.9$
• D. $409.8$

Answer 1

Answer: (D)

$409.8$

Given, $AB=30$, $\angle P={30}^{\circ }$, $\angle Q={45}^{\circ }$

In $△APB$,

$\tan P=\frac{P}{B}$

$\tan 30=\frac{AB}{PB}$

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

$PB=150\sqrt{3}$

In $△ABQ$,

$\tan Q=\frac{P}{B}$

$\tan 45=\frac{AB}{BQ}$

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

$BQ=150$

Thus, $AB=PB+BQ$

$AB=150\sqrt{3}+150$

$AB=409.8$