Question 254089: My geometry teacher today gave us a lesson on the 45-45-90 rule and the 30-60-90 rules. How do you solve for the hypotenuse of the 45-45-90 rule (hyp = leg * square root of 2) and the long leg of the 30-60-90 rule (short leg * square root of 3 = long leg)?
Answer by MRperkins(300)   (Show Source):
You can put this solution on YOUR website! You are using right triangles, so you can always use the pythagorean theorem. That is how these rules are created in the first place. the first one is already solved for the Hyp. You can use basic algebra on all of this, so you could say (short leg)^2+(long leg)^2=hyponetuse^2
Isoolate what you want to find, and then take the square root of it.
Let s=short leg
let l=long leg
let H=hypotenuse
then we are told s*square root of 3=l
so put this into your formula and you could say s^2+(s(sqrt of 3))^2=H^2
so s^2+3s^2=H^2
so 4s^2=H^2
take the square root of both sides and you get
2s=H
Remember that s is the length of the short side. Therefore, the Hypotenuse is 2 times the length of the short side.
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This is basically the proof of this theorem.
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If you want more help, then email me at justin.sheppard.tech@hotmail.com
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Justin
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