find vw.\nwrite your answer as an integer or as a decimal rounded to the nearest tenth.\nvw =

Explanation:

Step1: Identify the trigonometric relation

In right - triangle $VWX$, we know the hypotenuse $XW = 4$ and we want to find the side $VW$ opposite to the angle $\angle{X}=49^{\circ}$. We use the sine function since $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. $\sin(X)=\frac{VW}{XW}$

Step2: Substitute the known values

We know that $X = 49^{\circ}$ and $XW = 4$. So, $\sin(49^{\circ})=\frac{VW}{4}$. $VW = 4\times\sin(49^{\circ})$

Step3: Calculate the value

We know that $\sin(49^{\circ})\approx0.7547$. Then $VW=4\times0.7547 = 3.0188$. Rounding to the nearest tenth, $VW\approx3.0$.

Answer:

$3.0$