SOLUTION: I have been out of high school and college for over 4 years now...so I used to know the answer, but we are far from it now! I am looking for the "rules" or "formula" or "whatever"

Algebra ->  Algebra  -> Triangles -> SOLUTION: I have been out of high school and college for over 4 years now...so I used to know the answer, but we are far from it now! I am looking for the "rules" or "formula" or "whatever"      Log On

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Question 147089: I have been out of high school and college for over 4 years now...so I used to know the answer, but we are far from it now! I am looking for the "rules" or "formula" or "whatever" that makes this a correct statement. You have a triangle with a right angle. Side A =3ft Side B=4ft (side A and B are connected by the right angle). We know that side C (the hypotonus) =5ft. I want this equation in a larger term (ie Side A=10ft Side B=20ft what is side C) Thanks so much for your help! I actually miss doing this on a regular basis! I loved math in high school, and now it just helping my dad build a cabin. Thanks again. Michelle Wagner
Found 2 solutions by jim_thompson5910, solver91311:
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
We basically have this triangle set up:

drawing%28500%2C500%2C-0.5%2C2%2C-0.5%2C3.2%2C%0D%0A%0D%0Aline%280%2C0%2C0%2C3%29%2C%0D%0Aline%280%2C3%2C2%2C0%29%2C%0D%0Aline%282%2C0%2C0%2C0%29%2C%0D%0Alocate%28-0.2%2C1.5%2C10%29%2C%0D%0Alocate%281%2C-0.2%2C20%29%2C%0D%0Alocate%281%2C2%2Cx%29%0D%0A%29
Since we can see that the triangle has legs of 10 and 20 with a hypotenuse of x, we can use Pythagoreans theorem to find the unknown side.


Pythagoreans theorem:

a%5E2%2Bb%5E2=c%5E2 where a and b are the legs of the triangle and c is the hypotenuse



10%5E2%2B20%5E2=x%5E2 Plug in a=10, b=20, and c=x. Now lets solve for x


1+0+0+%2B+4+0+0+=++x++%5E+2 Square each individual term



5+0+0+=++x++%5E+2 Combine like terms


s+q+r+t+%28+5+0+0+%29+=+s+q+r+t+%28++x++%5E+2+%29 Take the square root of both sides


Which approximates to...

22.3606797749979=x

So our answer is
x=22.3606797749979


which means that

C=22.3606797749979

It might make more sense to round to the nearest hundredth to get C=22.36


Now take the decimal portion 0.36 and multiply it by 12 to get 0.36*12=4.32

So the length of C is about 22 feet 4.32 inches

Answer by solver91311(12126) About Me  (Show Source):
You can put this solution on YOUR website!
Use the Pythagorean Theorem. For a right triangle where the legs are a and b, and the hypotenuse is c, c%5E2=a%5E2%2Bb%5E2, so c=sqrt%28a%5E2%2Bb%5E2%29.

For your example:
a=10 and b=20, c=sqrt%28%2810%29%5E2%2B%2820%29%5E2%29=sqrt%28100%2B400%29=sqrt%28500%29 roughly 22.36 feet or about 22 feet, 4 and 3/8 inches. That ought to be close enough for log cabin building.

To do the decimal to feet/inches conversion, take the decimal part of the measurement and multiply times 12. .36 X 12 = 4.328 roughly. Now compare the decimal part of that result to the following table:

1/8 = .125
1/4 = .250
3/8 = .375
1/2 = .500
5/8 = .625
3/4 = .750
7/8 = .875

Pick the decimal value closest to the decimal part of your calculation and use the corresponding fractional value. That gets you within 1/8 inch which should be close enough. .328 corresponds most closely with .375, so 3/8 inch. Putting it all back together: 22 feet, 4 and 3/8 inches.

Hope that helps