Question

Find whether it is possible or not to construct a $\Delta$ whose measures are $a=5,b=7,\sin A=3/4$

Answer 1

$\sin A=3/4$

using relation between sin and cos

$=>\cos A=\sqrt{1-9/16}=\pm \sqrt{7}/4$
Now using cosine rule,
$\cos A=\frac{b^2+c^2-a^2}{2bc}=\frac{24+c^2}{14c}=\pm \frac{\sqrt{7}}{4}$
$\Rightarrow 2c^2\pm 7\sqrt{7}c+48=0$
Discriminant of above quadratic is, $D=49\times 7-8\times 48=-41<0$
Hence with given set of information, no real triangle is possible.