SOLUTION: calculate (to the nearest foot) the hypotenuse of a right triangle in which one leg is 9ft and the other leg is 1 ft less than the hypotenuse. I set it up like this: (a-1)^2 +b^2=

Algebra ->  Triangles -> SOLUTION: calculate (to the nearest foot) the hypotenuse of a right triangle in which one leg is 9ft and the other leg is 1 ft less than the hypotenuse. I set it up like this: (a-1)^2 +b^2=      Log On


   

Question 661067: calculate (to the nearest foot) the hypotenuse of a right triangle in which one leg is 9ft and the other leg is 1 ft less than the hypotenuse. I set it up like this:
(a-1)^2 +b^2=9^2
a^2-2a+1+b^2= 81
I don't know what to do with the b^2
Found 2 solutions by ewatrrr, MathLover1:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

 one leg is 9ft and the other leg is 1 ft less than the hypotenusehighlight%28a%29

 Using the Pythagorean Theorem, This Info Sets UP...

 (a-1)^2 + 9^2 = a^2

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
let the hypotenuse of a right triangle be c
and one leg a which is 9ft
and the other leg b is 1+ft less than the hypotenuse c.
so, we have:
highlight%28a=9ft%29
c=b%2B1ft...=>b=c-1ft
use Pythagoras theorem:
c%5E2=a%5E2%2Bb%5E2...substitute a and b with given values
c%5E2=%289ft%29%5E2%2B%28c-1ft%29%5E2
c%5E2=81ft%5E2%2Bc%5E2-2cft%2B1ft%5E2
cross%28c%5E2%29=81ft%5E2%2Bcross%28c%5E2%29-2cft%2B1ft%5E2
0=81ft%5E2-2cft%2B1ft%5E2
2cft=81ft%5E2%2B1ft%5E2
cross%282%29c%2Across%28ft%29=cross%2882%2941ft%5Ecross%282%291
highlight%28c=41ft%29
now find b
b=c-1ft
b=41ft-1ft
highlight%28b=40ft%29

check:
c%5E2=a%5E2%2Bb%5E2.....when highlight%28a=9ft%29,b=highlight%2840ft%29,highlight%28c=41ft%29

%2841ft%29%5E2=%289ft%29%5E2%2B%2840ft%29%5E2
1681ft%5E2=81ft%5E2%2B1600ft%5E2
1681ft%5E2=1681ft%5E2