SOLUTION: Hi! So, in my geometry class we are learning about special right triangles. (30,60,90 and 45,45,90). I recently took a quiz over the information and I was stuck on one problem.

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Question 1066460: Hi!
So, in my geometry class we are learning about special right triangles. (30,60,90 and 45,45,90). I recently took a quiz over the information and I was stuck on one problem. There is a 30,60,90 triangle, with the long leg as 10 square root three, and the short leg as X. The hypotenuse is y. The problem wanted you to solve for x and y. I tried using the rule of: short leg= x, long leg=x square root three, and the hypotenuse= 2x. Using that rule I got x as 10 and y as 20. Unfortunately this wasn't the right answer, and I was wondering if you could work through the problem, step by step to help me understand how to use the 30,60,90 rule and how it applies to this problem.
Thank you so much!!
Found 3 solutions by josgarithmetic, ikleyn, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Think from what the 30-60-90 special triangle comes from. Or draw it. The altitude of equilateral triangle cuts into two right triangles each congruent, of this 30-60-90 special right triangle type.

The short leg length is half the hypotenuse length. If your short leg is x, and your hypotenuse is y, then you have y%2F2=x.

As for getting the actual value of either x or y, you should know what to do using the Pythagorean Theorem formula for right triangle.
%28longLeg%29%5E2%2B%28shortLeg%29%5E2=hypotenuse%5E2
%2810sqrt%283%29%29%5E2%2Bx%5E2=%282x%29%5E2
300%2Bx%5E2=4x%5E2
3x%5E2=300
x%5E2=100
highlight%28x=10%29

Short leg, x=10;
hypotenuse, y=2%2Ax=20.

Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.
In my geometry class we are learning about special right triangles. (30,60,90 and 45,45,90).
I recently took a quiz over the information and I was stuck on one problem. 

There is a 30,60,90 triangle, with the long leg as 10 square root three, and the short leg as X. The hypotenuse is y. 

The problem wanted you to solve for x and y. I tried using the rule of: 

            short leg= x, 
            long leg=x square root three, and 
            the hypotenuse= 2x.                     THIS RULE IS CORRECT.

Using that rule I got x as 10 and y as 20.          YOUR SOLUTION AND YOUR ANSWER ARE CORRECT.

Unfortunately this wasn't the right answer,         <<<---+++  This statement is WRONG.

and I was wondering if you could work through the problem, step by step to help me understand how to use the 30,60,90 rule 
and how it applies to this problem.

Your solution is correct.

Your answer is correct.


Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Hi!
So, in my geometry class we are learning about special right triangles. (30,60,90 and 45,45,90). I recently took a quiz over the information and I was stuck on one problem. There is a 30,60,90 triangle, with the long leg as 10 square root three, and the short leg as X. The hypotenuse is y. The problem wanted you to solve for x and y. I tried using the rule of: short leg= x, long leg=x square root three, and the hypotenuse= 2x. Using that rule I got x as 10 and y as 20. Unfortunately this wasn't the right answer, and I was wondering if you could work through the problem, step by step to help me understand how to use the 30,60,90 rule and how it applies to this problem.
Thank you so much!! 
In a 30-60-90 special triangle, if matrix%281%2C4%2C+Longer%2C+leg%2C+%22=%22%2C+10sqrt%283%29%29, then:



Shorter leg = matrix%281%2C4%2C+Longer%2C+leg%2C+%22%2A%22%2C+sqrt%283%29%29%2F3%29. In this case, we get: Shorter leg, or 

Hypotenuse, or 

Your answers appear to be CORRECT!