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# 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 beta01510101641.png

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Non-right triangles and trigonometry asked 2021-01-31

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 ## Answers (1) 2021-02-01
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^@)/1.751ZSK
$$\displaystyle{\sin{\alpha}}=\frac{{{1.6}\cdot{\sin{{41.253}}}^{\circ}}}{{1.751}}$$
$$\displaystyle{\sin{\alpha}}={0.60252}$$
$$\displaystyle\therefore\alpha={37.051}^{\circ}$$
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,
$$\displaystyle\alpha={37.051}^{\circ}$$
$$\displaystyle\beta={101.696}^{\circ}$$

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