Question

solve for x. round to the nearest tenth of a degree, if necessary.
answer attempt 1 out of 2
x =

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, for angle \(x\), the opposite side to \(x\) is \(ST = 5.2\) and the adjacent side is \(RS=3.2\). We use the tangent ratio \(\tan x=\frac{\text{opposite}}{\text{adjacent}}\). So, \(\tan x=\frac{5.2}{3.2}\).

Step2: Solve for \(x\)

We know that \(x = \tan^{- 1}(\frac{5.2}{3.2})\). First, calculate \(\frac{5.2}{3.2}=1.625\). Then, \(x=\tan^{-1}(1.625)\). Using a calculator, \(x\approx58.4^{\circ}\).

Answer:

\(58.4\)