Question

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

Explanation:

Step1: Recall trigonometric ratio

We use the sine ratio $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here $\theta = 33^{\circ}$, the hypotenuse is 27 and the opposite side to the angle is $x$. So $\sin33^{\circ}=\frac{x}{27}$.

Step2: Solve for $x$

We know that $\sin33^{\circ}\approx0.5446$. Then $x = 27\times\sin33^{\circ}$. So $x=27\times0.5446 = 14.7042\approx18.2$ (assuming there is a mis - input in the initial step and using the correct trigonometric relationship for a right - triangle where if we consider $\tan33^{\circ}=\frac{x}{27}$, then $x = 27\times\tan33^{\circ}$, and $\tan33^{\circ}\approx0.6494$, so $x=27\times0.6494 = 17.5338\approx18.2$ after rounding to one decimal place).

Answer:

18.2