Question

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

Explanation:

Step1: Identify trigonometric ratio

We use the sine function, since we know the hypotenuse $\sqrt{5}$, and $x$ is opposite the $30^\circ$ angle: $\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$

Step2: Substitute known values

$\sin(30^\circ)=\frac{x}{\sqrt{5}}$

Step3: Solve for $x$

Since $\sin(30^\circ)=\frac{1}{2}$, substitute and rearrange:
$x = \sqrt{5} \times \sin(30^\circ) = \sqrt{5} \times \frac{1}{2}$

Step4: Calculate and round

$\sqrt{5}\approx2.236$, so $x\approx\frac{2.236}{2}=1.118$, rounded to the nearest tenth is $1.1$

Answer:

$1.1$