Question

find vx.
write your answer as an integer or as a decimal rounded to the nearest tenth.
vx =
find trigonometric functions of special angles
solve proportions

Explanation:

Step1: Identify the triangle type and trigonometric ratio

We have a right - triangle \(VWX\) with \(\angle W = 90^{\circ}\), \(\angle X=59^{\circ}\), and \(WX = 3\). We want to find the length of the hypotenuse \(VX\). We can use the cosine function, which is defined as \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\) in a right - triangle. For \(\angle X\), the adjacent side to \(\angle X\) is \(WX\) and the hypotenuse is \(VX\). So \(\cos(59^{\circ})=\frac{WX}{VX}\).

Step2: Solve for \(VX\)

We know that \(WX = 3\) and \(\cos(59^{\circ})\approx0.5150\). From \(\cos(59^{\circ})=\frac{3}{VX}\), we can re - arrange the formula to solve for \(VX\): \(VX=\frac{3}{\cos(59^{\circ})}\).
Substitute the value of \(\cos(59^{\circ})\) into the formula: \(VX=\frac{3}{0.5150}\approx5.8\)

Answer:

\(5.8\)