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

Explanation:

Step1: Identify trig - ratio

In right - triangle $UVW$ with right - angle at $V$, we know the hypotenuse $UW = 3$ and we want to find the side $UV$ opposite to the angle $\angle W=42^{\circ}$. We use the sine function since $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. $\sin W=\frac{UV}{UW}$

Step2: Substitute values

Given $W = 42^{\circ}$ and $UW = 3$, we substitute into the sine formula: $UV=UW\times\sin W$ $UV = 3\times\sin42^{\circ}$

Step3: Calculate value

We know that $\sin42^{\circ}\approx0.6691$. Then $UV=3\times0.6691 = 2.0073$. Rounding to the nearest tenth, we get $UV\approx2.0$.

Answer:

$2.0$