Question

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

Answer 1

Answer:

$Hypotenuse=10$

Step-by-step explanation:

The missing figure is attached.

For this exercise you can use the following Trigonometric Identity:

$sin\alpha=\frac{opposite}{hypotenuse}$

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

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

$\alpha=60\°\\\\opposite=5\sqrt{3}$

Then, knowing these values you can substitute them into $sin\alpha=\frac{opposite}{hypotenuse}$:

$sin(60\°)=\frac{5\sqrt{3}}{x}$

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

This is:

$x*sin(60\°)=5\sqrt{3}\\\\x=\frac{5\sqrt{3}}{sin(60\°)}\\\\x=10$