Question

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

Answer 1

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,
\(\displaystyle\alpha={37.051}^{\circ}\)
\(\displaystyle\beta={101.696}^{\circ}\)