Question

solve the triangle. write each answer as an integer or as a decimal rounded to the nearest tenth. m∠t = ° t = v =

Explanation:

Step1: Find angle $T$

The sum of angles in a triangle is $180^{\circ}$. So $m\angle T=180^{\circ}-92^{\circ}- 50^{\circ}=38^{\circ}$.

Step2: Use the Law of Sines to find $t$

The Law of Sines states that $\frac{t}{\sin T}=\frac{v}{\sin V}=\frac{u}{\sin U}$. We know that $\frac{t}{\sin T}=\frac{13}{\sin U}$. Since $T = 38^{\circ}$, $U=92^{\circ}$ and the side opposite $U$ is $13$. So $t=\frac{13\sin T}{\sin U}=\frac{13\sin38^{\circ}}{\sin92^{\circ}}\approx\frac{13\times0.616}{0.999}\approx8.0$.

Step3: Use the Law of Sines to find $v$

Using the Law of Sines $\frac{v}{\sin V}=\frac{13}{\sin U}$. Since $V = 50^{\circ}$ and $U=92^{\circ}$, then $v=\frac{13\sin V}{\sin U}=\frac{13\sin50^{\circ}}{\sin92^{\circ}}\approx\frac{13\times0.766}{0.999}\approx10.0$.

Answer:

$m\angle T = 38^{\circ}$
$t\approx8.0$
$v\approx10.0$