Question

solve for $x$. round to the nearest tenth, if necessary.

Explanation:

Step1: Use cosine function

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(\theta = 50^{\circ}\), the adjacent side to the angle \(U\) is \(VU=x\), and the hypotenuse \(WU = 6.1\). So, \(\cos(50^{\circ})=\frac{x}{6.1}\).

Step2: Solve for \(x\)

Multiply both sides of the equation \(\cos(50^{\circ})=\frac{x}{6.1}\) by \(6.1\). We get \(x = 6.1\times\cos(50^{\circ})\).
Using a calculator, \(\cos(50^{\circ})\approx0.6428\). Then \(x=6.1\times0.6428\).
\(x = 6.1\times0.6428=3.92108\approx3.9\)

Answer:

\(x\approx3.9\)