Question

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

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle \( \triangle RST\) with right - angle at \(S\), \(\angle T = 53^{\circ}\), \(TS = 2.7\), and we want to find \(RS=x\). The trigonometric ratio \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 53^{\circ}\), the opposite side to \(\angle T\) is \(RS=x\) and the adjacent side to \(\angle T\) is \(TS = 2.7\). So, \(\tan(53^{\circ})=\frac{x}{2.7}\).

Step2: Solve for \(x\)

We know that \(\tan(53^{\circ})\approx1.33\). Then, from the equation \(x = 2.7\times\tan(53^{\circ})\). Substitute \(\tan(53^{\circ})\approx1.33\) into the equation: \(x=2.7\times1.33\).

$$x = 3.591$$

Answer:

\(x\approx3.6\)