Question

In a $\Delta ABC$, if $a=\sqrt{2},b=2,c=\sqrt{3}+1$, then $\angle A=$

• A. ${15}^{\circ }$
• B. ${30}^{\circ }$
• C. ${45}^{\circ }$
• D. None of these

Answer 1

The correct option is B ${30}^{\circ }$

Given that, $a=\sqrt{2},b=2$ and $c=\sqrt{3}+1$

Find the value of $\angle A=?$

We know that

$\cos A=\frac{b^2+c^2-a^2}{2bc}$

$\cos A=\frac{2^2+{(\sqrt{3}+1)}^2-{\left(\sqrt{2}\right)}^2}{2\times 2\times (\sqrt{3}+1)}$

$=\frac{4+{\left(\sqrt{3}\right)}^2+1^2+2\sqrt{3}-2}{4(\sqrt{3}+1)}$

$=\frac{6+2\sqrt{3}}{4(\sqrt{3}+1)}$

$=\frac{2\sqrt{3}(\sqrt{3}+1)}{4(\sqrt{3}+1)}$

$=\frac{\sqrt{3}}{2}$

$\cos A=\cos {30}^0$

$\angle A={30}^0$

Hence, it is complete solution.

Option $\left(B\right)$ is correct.