Question

find the length of side ( x ) to the nearest tenth.
answer attempt 1 out of 2
( x = )
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Explanation:

Step1: Identify trigonometric ratio

We use the sine function, since we know the opposite side to the 30° angle ($\sqrt{11}$) and $x$ is the hypotenuse. The sine formula is $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$.

Step2: Substitute known values

$\sin(30^\circ) = \frac{\sqrt{11}}{x}$
We know $\sin(30^\circ) = \frac{1}{2}$, so:
$\frac{1}{2} = \frac{\sqrt{11}}{x}$

Step3: Solve for $x$

Rearrange the equation to isolate $x$:
$x = 2 \times \sqrt{11}$
Calculate $\sqrt{11} \approx 3.3166$, so $x \approx 2 \times 3.3166 = 6.6332$

Step4: Round to nearest tenth

Round 6.6332 to one decimal place: $x \approx 6.6$

Answer:

$x = 6.6$