Question

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

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle \( \triangle VWT\) with right - angle at \(W\), we know the adjacent side to angle \(T\) (\(WT = 96\)) and we need to find the opposite side to angle \(T\) (\(x\)). The trigonometric ratio that relates the opposite and adjacent sides of an angle in a right - triangle is the tangent ratio. The formula for tangent is \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 52^{\circ}\), the opposite side is \(x\) and the adjacent side is \(96\). So, \(\tan(52^{\circ})=\frac{x}{96}\).

Step2: Solve for \(x\)

We can rewrite the equation \(\tan(52^{\circ})=\frac{x}{96}\) as \(x = 96\times\tan(52^{\circ})\).
We know that \(\tan(52^{\circ})\approx1.2799\) (using a calculator). Then \(x=96\times1.2799\).

$$x = 96\times1.2799=122.8704$$

Answer:

\(122.9\)