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

Question

asked Dec 17, 2021 187k views

1 Answer

Beldi Anouar · Answer 1 · 2021-12-21T02:35:53+0000

Answer:

Explanation:

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:

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