Question

The right triangle above, what is the length of the hypotenuse?19.214.18.532.0

Answer 1

Hypotenuse = 32.0

Step-by-step explanation:

We were given a right angle with the following:

`\begin{gathered} \theta=31^(\circ) \\ opposite\text{ }side=16.5 \\ hypotenuse=? \end{gathered}`

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:

`\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))=(16.5)/(hypotenuse) \\ \text{Cross multiply, we have:} \\ hypotenuse*sin(31^(\circ))=16.5 \\ hypotenuse=(16.5)/(sin(31^(\circ))) \\ hypotenuse=32.0365\approx32.0 \\ hypotenuse=32.0 \\ \\ \therefore hypotenuse=32.0 \end{gathered}`

Therefore, the hypotenuse is 32.0