Question

4.
what is the value of x? round your answer to the nearest tenths.

Explanation:

Step1: Identify trigonometric ratio

We use sine for $\angle E$: $\sin(30^\circ) = \frac{LO}{LE}$

Step2: Calculate opposite side length

$LO = LE \times \sin(30^\circ) = 12 \times 0.5 = 6$

Step3: Use Pythagorean theorem

$x = \sqrt{LE^2 - LO^2} = \sqrt{12^2 - 6^2}$

Step4: Compute and round result

$\sqrt{144 - 36} = \sqrt{108} \approx 10.4$

Answer:

10.4