Question

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

Explanation:

Step1: Use sine - function definition

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 33^{\circ}$, the opposite side to the angle $33^{\circ}$ is $x$, and the hypotenuse is $27$. So, $\sin33^{\circ}=\frac{x}{27}$.

Step2: Solve for $x$

We know that $\sin33^{\circ}\approx0.5446$. Then $x = 27\times\sin33^{\circ}$. Substituting the value of $\sin33^{\circ}$, we get $x=27\times0.5446 = 14.7042\approx18.1$.

Answer:

$x\approx18.1$