Question

If $a=2\sqrt{2},b=6,A={45}^{}$, then

• A. No triangle is possible
• B. One triangle is possible
• C. Two triangles are possible
• D. Either no triangle or two triangles are possible

Answer 1

The correct option is A No triangle is possible

Using sine rule,
$\frac{a}{\sin A}=\frac{b}{\sin B}$
$\Rightarrow \frac{2\sqrt{2}}{\sin {45}^{}}=\frac{6}{\sin B}$
$\Rightarrow \sin B=\frac{6}{2\sqrt{2}}\times \frac{1}{\sqrt{2}}$
$=\frac{6}{4}=\frac{3}{2}>1$
Which is not possible.
Hence, no triangle is possible.