Question

In the right triangle above, what is the length of the hypotenuse?Diagram19.214.18.532.0

Answer 1

Given:

Length of leg = 16.5

Angle = 31 degrees.

Let's find the length of the hypotenuse.

To find the length of the hypotenuse, apply the trigonometric ratio formula for sine:

`sin\theta=(opposite)/(hypotenuse)`

Where:

Opposite side is the side opposite the angle = 16.5

θ is the angle = 31 degrees.

Hence, we have:

`\begin{gathered} sin31=(16.5)/(hyotenuse) \\ \\ hypotenuse=(16.5)/(sin31) \\ \\ hypotenuse=(16.5)/(0.515) \\ \\ hypotenuse=32.03 \end{gathered}`

Therefore, the length of the hypotenuse is 32.0 units.

ANSWER:

32.0