Question

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

• A. no triangle exists
• B. only one triangle exists
• C. two triangles are possible
• D. either no triangle or two triangles are possible

Answer 1

The correct option is A no triangle exists

Using cosine formula in the triangle,
$c^2+b^2-2cb\cos A=a^2$
$\therefore c^2+36-\frac{12}{\sqrt{2}}c=8$
$\therefore c^2-6\sqrt{2}c+28=0$
For this quadratic in $c$,
$D<0$
$\therefore$ No $c$ is possible i.e. no triangle is possible.Correct option 'A'