Question

In the given figure, $\angle PAB={60}^o$ and $\angle CAB={30}^o$ and $PB=75m.$ Find $BC.$

• A. $22\sqrt{3}$
• B. $25\sqrt{3}$
• C. $5\sqrt{3}$
• D. $20\sqrt{3}$

Answer 1

The correct option is B $25\sqrt{3}$

REF.Image

$\angle CAB={30}^{\circ }$, $AB=75m$

in triangle ABC

$\tan \angle CAB=\frac{BC}{AB}$

$\tan {30}^o=\frac{BC}{75}$

$\frac{1}{\sqrt{3}}=\frac{BC}{75}$

$\Rightarrow BC=\frac{75}{\sqrt{3}}=\frac{25\times 3\sqrt{3}}{\sqrt{3}}=25\sqrt{3}m$

$\therefore BC=25\sqrt{3}m$.