Solve each of the following triangles. If there are two

Carolyn Moore 2021-11-25 Answered
Solve each of the following triangles. If there are two triangles, solve both. Round angle measurements to one decimal place and side lengths to two decimal places. \(\displaystyle{a}={10},\ {b}={12},\ {c}={7}\)
a=?
B=?
y=?

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Expert Answer

Theirl1972
Answered 2021-11-26 Author has 8149 answers
Step 1
Given: \(\displaystyle{a}={10},\ {b}={12},\ {c}={7}\)
\(\displaystyle\alpha={{\cos}^{{-{1}}}{\left({\frac{{{b}^{{{2}}}+{c}^{{{2}}}-{a}^{{{2}}}}}{{{2}{b}{c}}}}\right)}}\)
\(\displaystyle={{\cos}^{{-{1}}}{\left({\frac{{{93}}}{{{168}}}}\right)}}\)
Step 2
\(\displaystyle\alpha={56.4}^{{\circ}}\)
\(\displaystyle{B}={{\cos}^{{-{1}}}{\left({\frac{{{a}^{{{2}}}+{c}^{{{2}}}-{b}^{{{2}}}}}{{{2}{a}{c}}}}\right)}}\)
\(\displaystyle={{\cos}^{{-{1}}}{\left({\frac{{{5}}}{{{140}}}}\right)}}\)
\(\displaystyle{B}={87.9}^{{\circ}}\)
\(\displaystyle{y}={{\cos}^{{-{1}}}{\left({\frac{{{a}^{{{2}}}+{b}^{{{2}}}-{c}^{{{2}}}}}{{{2}{a}{b}}}}\right)}}\)
\(\displaystyle={{\cos}^{{-{1}}}{\left({\frac{{{195}}}{{{240}}}}\right)}}\)
\(\displaystyle{y}={35.7}^{{\circ}}\)
Answer:
\(\displaystyle\alpha={56.4}^{{\circ}}\)
\(\displaystyle{B}={87.9}^{{\circ}}\)
\(\displaystyle{y}={35.7}^{{\circ}}\)
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