Consider the non-triangle shown below that has side lenghts of 1.6, 1.751 and 2.6 cm and interior angle measures of 0.72, alpha and beta degrees.What is value of alpha and beta01510101641.png

According to sine law:
${\displaystyle \frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}}$
Thus, $(\sin \alpha )/1.6=(\sin {41.253}^{@})/1.751$
${\displaystyle \sin \alpha =\frac{1.6\cdot {\sin 41.253}^{\circ }}{1.751}}$
${\displaystyle \sin \alpha =0.60252}$
${\displaystyle \therefore \alpha ={37.051}^{\circ }}$
Now, using triangle property
${\displaystyle A+B+C={180}^{\circ }}$
${\displaystyle \alpha +\beta +41.253={180}^{\circ }}$
${\displaystyle 37.051+\beta ={180}^{\circ }-{41.253}^{\circ }}$
${\displaystyle \beta =138.747-37.051}$
${\displaystyle \therefore \beta ={101.696}^{\circ }}$
Therefore,
${\displaystyle \alpha ={37.051}^{\circ }}$
${\displaystyle \beta ={101.696}^{\circ }}$