What is the length of the hypotenuse in the 306090 triangle shown below ?
Mathematics
helmwauteshia10
Question
What is the length of the hypotenuse in the 306090 triangle shown below ?
1 Answer

1. User Answers luisejr77
Answer:
[tex]Hypotenuse=10[/tex]
Stepbystep explanation:
The missing figure is attached.
For this exercise you can use the following Trigonometric Identity:
[tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex]
Let be "x" the hypotenuse of this right triangle.
You can identify from the figure that, in this case:
[tex]\alpha=60\°\\\\opposite=5\sqrt{3}[/tex]
Then, knowing these values you can substitute them into [tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex]:
[tex]sin(60\°)=\frac{5\sqrt{3}}{x}[/tex]
Finally, you need to solve for "x" in order to find the lenght of the hypotenuse.
This is:
[tex]x*sin(60\°)=5\sqrt{3}\\\\x=\frac{5\sqrt{3}}{sin(60\°)}\\\\x=10[/tex]