Answer:
Hypotenuse = 32.0
Explanation:
We were given a right angle with the following:
[tex]\begin{gathered} \theta=31^{\circ} \\ opposite\text{ }side=16.5 \\ hypotenuse=? \end{gathered}[/tex]
We have one know side, one known angle & one unknown side. To obtain the value of the unknown side, we will use the Trigonometric Ratio (SOHCAHTOA). In this case, we will use "SOH" as shown below:
[tex]\begin{gathered} SOH\Rightarrow sin\theta=\frac{opposite\text{ }side}{hypotenuse} \\ \begin{equation*} sin\theta=\frac{opposite\text{ }side}{hypotenuse} \end{equation*} \\ \text{Substitute the known variables into the formula, we have:} \\ sin(31^{\circ})=\frac{16.5}{hypotenuse} \\ \text{Cross multiply, we have:} \\ hypotenuse*sin(31^{\circ})=16.5 \\ hypotenuse=\frac{16.5}{sin(31^{\circ})} \\ hypotenuse=32.0365\approx32.0 \\ hypotenuse=32.0 \\ \\ \therefore hypotenuse=32.0 \end{gathered}[/tex]
Therefore, the hypotenuse is 32.0
