SOLUTION: how do you find the length of the side of an right angle triangle when you know the length of one side

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Question 575090: how do you find the length of the side of an right angle triangle when you know the length of one side
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
If all you know is the length of one side and that there is a right angle, you do not have enough information. You cannot solve the triangle because there are infinite triangles that would fit the same information.
Here are two right triangles with the same length for the side marked.
If you had a little more information, maybe you could find solutions.
For example:
You could find the length of all sides of an isosceles right triangle if you know the length of one side. Being an isosceles right triangle means having angles measuring 90, 45, and 45 degrees, so the word isosceles gives you a lot of information.
Just having the measure of an angle and a side would help too.
For example, if the angle opposite a side of length 5 measures 30 degrees:
You would know that
sin%28angle%29=%28opposite_leg%29%2Fhypotenuse
sin%2830%5Eo%29=1%2F2
So 1%2F2=5%2Fhypotenuse --> hypotenuse+=5%2A2=10
Then you could use Pythagoras theorem to find the length of the other leg.
Calling the length of the other leg x, Pythagoras theorem says
5%5E2%2Bx%5E2=10%5E2 --> 25%2Bx%5E2=100 --> x%5E2=100-25 --> x%5E2=75 --> x=sqrt%2875%29