Question

If $A={30}^{\circ },a=7$ and $b=8$ in $\Delta ABC$ then find the number of triangles that can be constructed.

Answer 1

Given, $A={30}^o,a=7,b=8$

We have $\frac{a}{\sin A}=\frac{b}{\sin B}$ or
$\sin B=\frac{b\sin A}{a}=\frac{8\sin {30}^{\circ }}{7}=\frac{4}{7}$
Thus,we have,$b>a>b\sin A$

Hence, angle B has two values given by $\sin B=4/7$
Thus two triangles are possible with the given information.