Consider the non-right triangle shown below that has lengths of 1.6, 1.751 and 2

impresijuzj 2021-11-18 Answered
Consider the non-right triangle shown below that has lengths of 1.6, 1.751 and 2.6 cm and interior angle measures of 0.72, \(\displaystyle\alpha\), and \(\displaystyle\beta\) degrees.
image
a) What is the value of \(\displaystyle\alpha\)?
b) What is the value of \(\displaystyle\beta\)?

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Expert Answer

Forneadil
Answered 2021-11-19 Author has 1175 answers
Step 1
Let,
\(\displaystyle{a}={1.6}{c}{m}\)
\(\displaystyle{b}={2.6}{c}{m}\)
\(\displaystyle{c}={1.751}{c}{m}\)
And,
\(\displaystyle{A}=\alpha,\ {B}=\beta,\ {C}={41.253}^{{\circ}}\)
According to sine law:
\(\displaystyle{\frac{{{\sin{{A}}}}}{{{a}}}}={\frac{{{\sin{{B}}}}}{{{b}}}}={\frac{{{\sin{{C}}}}}{{{c}}}}\)
Step 2
Thus,
\(\displaystyle{\frac{{{\sin{\alpha}}}}{{{1.6}}}}={\frac{{{\sin{{41.253}}}^{{\circ}}}}{}}\)
\(\displaystyle{\sin{\alpha}}={\frac{{{1.6}\times{\sin{{41.253}}}^{{\circ}}}}{{{1.751}}}}\)
\(\displaystyle{\sin{\alpha}}={0.60252}\)
\(\displaystyle\therefore\alpha={37.051}^{{\circ}}\)
Now, using triangle property
\(\displaystyle{A}+{B}+{C}={180}^{{\circ}}\)
\(\displaystyle\alpha+\beta+{41.253}={180}^{{\circ}}\)
\(\displaystyle{37.051}+\beta={180}^{{\circ}}-{41.253}^{{\circ}}\)
\(\displaystyle\beta={138.747}-{37.051}\)
\(\displaystyle\therefore\beta={101.696}^{{\circ}}\)
Step 3
Therefore,
\(\displaystyle\alpha={37.051}^{{\circ}}\)
\(\displaystyle\beta={101.696}^{{\circ}}\)
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