Question

What is the length of the hypotenuse in the 30-60-90 triangle shown below ?

Answer 1

`Hypotenuse=10`

Explanation:

The missing figure is attached.

For this exercise you can use the following Trigonometric Identity:

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

Let be "x" the hypotenuse of this right triangle.

You can identify from the figure that, in this case:

`\alpha=60\°\\\\opposite=5√(3)`

Then, knowing these values you can substitute them into
`sin\alpha=(opposite)/(hypotenuse)`:

`sin(60\°)=(5√(3))/(x)`

Finally, you need to solve for "x" in order to find the lenght of the hypotenuse.

This is:

`x*sin(60\°)=5√(3)\\\\x=(5√(3))/(sin(60\°))\\\\x=10`