Question

solve for the side
set up an equation, then solve for x. be accurate to within one decimal.

Explanation:

Step1: Use sine function

$\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, here $\theta = 12^{\circ}$, opposite side is $x$ and hypotenuse is $11$. So $\sin(12^{\circ})=\frac{x}{11}$.

Step2: Solve for $x$

$x = 11\times\sin(12^{\circ})$. Since $\sin(12^{\circ})\approx0.2079$, then $x = 11\times0.2079\approx2.3$.

Answer:

$x \approx 2.3$