# Solve each of the following triangles. If there are two

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=?

• Questions are typically answered in as fast as 30 minutes

### Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Theirl1972
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
$$\displaystyle\alpha={56.4}^{{\circ}}$$
$$\displaystyle{B}={{\cos}^{{-{1}}}{\left({\frac{{{a}^{{{2}}}+{c}^{{{2}}}-{b}^{{{2}}}}}{{{2}{a}{c}}}}\right)}}$$
$$\displaystyle={{\cos}^{{-{1}}}{\left({\frac{{{5}}}{{{140}}}}\right)}}$$
$$\displaystyle{B}={87.9}^{{\circ}}$$
$$\displaystyle{y}={{\cos}^{{-{1}}}{\left({\frac{{{a}^{{{2}}}+{b}^{{{2}}}-{c}^{{{2}}}}}{{{2}{a}{b}}}}\right)}}$$
$$\displaystyle={{\cos}^{{-{1}}}{\left({\frac{{{195}}}{{{240}}}}\right)}}$$
$$\displaystyle{y}={35.7}^{{\circ}}$$
$$\displaystyle\alpha={56.4}^{{\circ}}$$
$$\displaystyle{B}={87.9}^{{\circ}}$$
$$\displaystyle{y}={35.7}^{{\circ}}$$