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

Explanation:

Step1: Identify the trig - ratio

In right - triangle $VWX$, we know the side $VW = 7.8$ and the angle $\angle X=63^{\circ}$, and we want to find the hypotenuse $VX$. We use the cosine function since $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\cos X=\frac{WX}{VX}$, and we can also use the sine function $\sin X=\frac{VW}{VX}$.

Step2: Apply the sine formula

We know that $\sin X=\frac{VW}{VX}$, where $X = 63^{\circ}$ and $VW = 7.8$. So, $\sin63^{\circ}=\frac{7.8}{VX}$. Since $\sin63^{\circ}\approx0.891$, we can rewrite the equation as $0.891=\frac{7.8}{VX}$.

Step3: Solve for $VX$

Cross - multiply to get $VX\times0.891 = 7.8$. Then $VX=\frac{7.8}{0.891}\approx8.8$.

Answer:

$8.8$