Question

find the side labeled x. x =

Explanation:

Step1: Use sine - function definition

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 30^{\circ}$, the opposite side to the $30^{\circ}$ angle is $x$ and the hypotenuse is 11. So, $\sin30^{\circ}=\frac{x}{11}$.

Step2: Substitute the value of $\sin30^{\circ}$

We know that $\sin30^{\circ}=\frac{1}{2}$. Substituting this into the equation $\sin30^{\circ}=\frac{x}{11}$, we get $\frac{1}{2}=\frac{x}{11}$.

Step3: Solve for $x$

Cross - multiply the equation $\frac{1}{2}=\frac{x}{11}$ to get $2x = 11$. Then $x=\frac{11}{2}=5.5$.

Answer:

$5.5$