Question

If $a=2\sqrt{2},b=6,A=45°,$then

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

Answer 1

The correct option is A

No triangle is possible

Explanation for correct option :

We have given

$$\begin{gathered} a=2\sqrt{2}, \\ b=6, \\ A=45° \end{gathered}$$

By putting the values of

$$\begin{gathered} a=2\sqrt{2}, \\ b=6, \\ A=45° \end{gathered}$$

From sine rule,

$$\begin{gathered} \Rightarrow \frac{\sin \left(45°\right)}{2\sqrt{2}}=\frac{\sin \left(B\right)}{6} \\ \Rightarrow \frac{1\times 6}{2\sqrt{2}\times \sqrt{2}}=\sin \left(B\right) \\ \Rightarrow \frac{3}{2}=\sin \left(B\right) \end{gathered}$$ $\frac{\mathbf{s}\mathbf{i}\mathbf{n}\left(A\right)}{\mathbf{a}}\mathbf{=}\frac{\mathbf{s}\mathbf{i}\mathbf{n}\left(B\right)}{\mathbf{b}}$

$\sin \left(B\right)$ cannot be great then$1$.

So, the above case is impossible.

Hence, the correct option is (A).