Geometry question with a^2 + b^2 = c^2?

dont worry , this is not a homework question, its a i took this back in high school now i actually need to use it for woodwork, lol.





Assume you have a perfect right triangle. Both sides are 5 inches long.





a^2 + b^2 = c^2


5^2 + 5^2 = c^2


c^2 = 50


**** assume when u say radical its is V-- ****


c = 50^(.5) or expressed as V--50





When I take 50^(.5) i end up with 7.071 ~~





So according to this the length of c is 7.071~~ inches





(A) is this the correct length of c?


(B) if i want to set c ( the hypotenuse) to a certain value of a right triangle, what is the formula to figure out the sides length.





this is my crack at it





Assume the hypotenuse is 10


a^2 + b^2 = 10


a = b


a^2 + a^2 = 10


2(a^2) = 10


????????

Geometry question with a^2 + b^2 = c^2?
a) correct





b) that leads to a^2 = 10/2 = 5





therefore a = V5





(a calculator would reveal 2 . something here)





dont be afraid of strange numbers in your results - that happens in real life examples more than you think. In school textbook examples the questions are geared to give answers that are well rounded and 'nice' because the focus is on conveying the method of calculation





some good whole number right angled triangles are





(a, b, c)





3,4,5


6,8,10


9,12,15





etc multiplying the first set by the same number each time





another common one is





5,12,13
Reply:Assume the hypotenuse is 10


a^2 + b^2 = 10 %26lt;%26lt;-------remember the formula is





a^2+b^2=c^2





so if you want your hyp to be 10 then the equation would be





a^2+b^2=10^2





a^2+b^2=100





then continue as you did above, and you will get it right.


7.071 is the correct answer for the first part
Reply:A) The length c should be 7.071 inches. Since 1/16 of an inch is .0625, you want a bit more than 7 1/16 inches.





B) Notice that you should have 10^2=100, not just 10. Next, get a^2=100/2=50, so


a=sqrt(50)=7.071.
Reply:You almost have it but you forgot to square the hypotenuse.





so 2(a^2) = 10^2 = 100





a^2 = 50





a = 50 ^ (0.5)
Reply:In the first scenario, c = 7.071~~ inches.





In the 2nd scenario, you are on the right track (if you want both sides to be equal).


2(a^2) = 10


(2(a^2))/2 = 10/2


a^2 = 5


a = 2.236 inches
Reply:1.) Your calculations are correct and precise at the answer.





2.) The formula (based on your calculations) are "If a=b, then a squ.=b squ., so a squ +b squ= 2 a squ., so c squ. = 2 a squ. then, .5 c squ = a squ, in short. a squ will equal one-half of c squ.