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

Explanation:

Step1: Identify the trig - ratio

In right - triangle $\triangle LKJ$, we know the opposite side ($JK = 3.6$) and the hypotenuse ($LJ=5.4$) with respect to angle $x$. We use the sine ratio $\sin x=\frac{\text{opposite}}{\text{hypotenuse}}$. So, $\sin x=\frac{3.6}{5.4}$.

Step2: Simplify the ratio

$\frac{3.6}{5.4}=\frac{36}{54}=\frac{2}{3}\approx0.6667$. So, $\sin x\approx0.6667$.

Step3: Find the angle

To find $x$, we take the inverse sine (arcsine) of $0.6667$. That is $x = \sin^{-1}(0.6667)$. Using a calculator, $x=\sin^{-1}(0.6667)\approx41.8^{\circ}$.

Answer:

$41.8$