Question

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

Explanation:

Step1: Use trigonometric ratio

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 50^{\circ}\), the opposite side to \(\angle V\) is \(WT = 7.7\) and the adjacent side is \(WV=x\). So, \(\tan V=\frac{WT}{WV}\).

Step2: Substitute the values

Since \(V = 50^{\circ}\) and \(WT = 7.7\), we have \(\tan50^{\circ}=\frac{7.7}{x}\). Then \(x=\frac{7.7}{\tan50^{\circ}}\).
We know that \(\tan50^{\circ}\approx1.191753592\).

Step3: Calculate the value of \(x\)

\(x=\frac{7.7}{1.191753592}\approx6.5\)

Answer:

\(x\approx6.5\)