Answer
This type of triangle with the given measurements does not exist.
Work Step by Step
The given angles and side of the triangle are provided below:
$A=65{}^\circ,a=6,b=7$
Using the law of sines, we will find the angle B of the triangle. That is,
$\begin{align}
& \frac{\sin A}{a}=\frac{\sin B}{b} \\
& \frac{\sin 65{}^\circ }{6}=\frac{\operatorname{sinB}}{7}
\end{align}$
Therefore,
$\begin{align}
& \operatorname{sinB}=7\times \frac{\sin 65{}^\circ }{6} \\
& \operatorname{sinB}=1.0574
\end{align}$
The function sine can’t exceed the value 1. Therefore, $\operatorname{sinB}=1.0574$ is not possible.
Thus, there does not exist any triangle of this type with the given measurements.
