Answer:
[tex]\begin{gathered} a=2.08 \\ b=11.82 \\ m\lt B=80 \end{gathered}[/tex]
Step-by-step explanation:
To solve the missing sides using trigonometric ratios, which are described by the following equations:
[tex]\begin{gathered} sin\left(angle\right)=\frac{opposite}{hypotenuse} \\ cos\left(angle\right)=\frac{adjacent}{hypotenuse} \\ tan\left(angle\right)=\frac{opposite\text{ }}{adjacent} \end{gathered}[/tex]
Then, for the missing sides, use the sin and cos relationship:
[tex]\begin{gathered} sin\left(10\right)=\frac{a}{12} \\ a=12*sin\left(10\right) \\ a=2.08 \\ \\ cos\left(10\right)=\frac{b}{12} \\ b=12*cos\left(10\right) \\ b=11.817 \\ \text{ Rounding to the nearest hundredth:} \\ b=11.82 \end{gathered}[/tex]
Since all intern angles of a triangle must add up to 180 degrees, solve for angle ''B'':
[tex]\begin{gathered} m
