# Perimeter of right triangle?

• Jan 9th 2012, 07:08 AM
Matt93
Perimeter of right triangle?
I'm doing a study guide and one question that has had me stumped is this: you have to find the perimeter of a right triangle with a hypotenuse of 10 square root of 3 and a measurement of 30. I know I'm supposed to follow the 30 60 90 format, but.....
• Jan 9th 2012, 07:34 AM
MarkFL
Re: Perimeter of right triangle???
In a 30-60-90 triangle, what are the ratios of the sides to one another?
• Jan 9th 2012, 07:46 AM
Matt93
Re: Perimeter of right triangle???
Well, 60 degrees is across from the 10 square root of 3 and the 30 degrees is across from B (there's no number)
• Jan 9th 2012, 07:56 AM
MarkFL
Re: Perimeter of right triangle???
The hypotenuse is opposite the 90° angle and is given as $\displaystyle 10\sqrt{3}$.

The 30° angle is opposite the shorter leg, and the 60° angle is opposite the longer leg. Since you state you are supposed to use the 30-60-90 format, I took that to mean you have been given the ratios of the sides to one another in such a triangle. If not, we can use some basic trigonometry to get these ratios:

Let a be the shorter leg, b be the longer leg, and c the hypotenuse. Using the definition:

$\displaystyle \sin\theta=\frac{\text{opposite}}{\text{hypotenuse }}$

on the 3 angles, what do you find?