find v. write your answer as an integer or as a decimal rounded to the nearest tenth. v =

Explanation:

Step1: Find angle T

The sum of angles in a triangle is 180°. So, $\angle T=180^{\circ}-(54^{\circ} + 83^{\circ})=43^{\circ}$.

Step2: Use the Law of Sines

The Law of Sines states that $\frac{v}{\sin V}=\frac{u}{\sin U}=\frac{t}{\sin T}$. We know $\angle V = 54^{\circ}$, $\angle U=83^{\circ}$, $\angle T = 43^{\circ}$ and side opposite $\angle T$ is not given, side opposite $\angle U$ is $7$. We want to find $v$ (side opposite $\angle V$). So, $\frac{v}{\sin54^{\circ}}=\frac{7}{\sin43^{\circ}}$.

Step3: Solve for v

$v=\frac{7\times\sin54^{\circ}}{\sin43^{\circ}}$. Since $\sin54^{\circ}\approx0.809$ and $\sin43^{\circ}\approx0.682$, then $v=\frac{7\times0.809}{0.682}=\frac{5.663}{0.682}\approx8.3$.

Answer:

$8.3$