# 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

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 beta

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Jayden-James Duffy

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