Question

$ABC$ is an isosceles triangle right angled at $A$. Force of magnitude $2\sqrt{2},5$ and $6$ act along $\overline{BC},\overline{CA},\overline{AB}$ respectively. The magnitude of their resultant force is

• A. $4$
• B. $5$
• C. $11+2\sqrt{2}$
• D. $30$

Answer 1

The correct option is B $5$

REF.Image.

$AB=AC\Rightarrow \angle B=\angle C$

And $\angle B+\angle C+90-180$

$\Rightarrow \angle B=\angle C={45}^{\circ }$

Taking components of $2\sqrt{2}$

$2\sqrt{2}cos45=2\sqrt{2}\times \frac{1}{\sqrt{2}}=2$

$2\sqrt{2}sin45=2\sqrt{2}\times \frac{1}{\sqrt{2}}=2$

$\Rightarrow$ Resultant =$\sqrt{16+9}=5N$

$\Rightarrow \left(B\right)$