Pythagorean Theorem

DanaAJames

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Oct 29, 2014
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I know that a2+b2=c2. I also that c is the hypotenuse of a right triangle and a and b are the legs of a right triangle. I know how to work backwards (for example finding b from just the values of c and a, or just the value of c). However, I am still trying to figure out how to find what b is. I keep getting the wrong answer, and suspect it is a simple arithmetic error. But, here is what the problem is:

a= 110
c= 140

Edit: So, here is what I have:
11022+b2=14022
12100+b2=19600
-12100 -12100
__ _____
✔️b2=✔️7500
__
b=2500✔️3
Edit: I have checked with 10 other people (7 in my class, 3 in my family) and all of them got that answer. Everyone but my teacher, who marked it wrong. I'm pretty sure everyone else got that as well.


Thank you for your help.
 
Last edited:
I know how to...[find] b from just the values of c and a.... However, I am still trying to figure out how to find what b is.
I'm sorry, but I don't understand. Do you know, or do you not know, how to find the value of b, given the values of a and c?

I keep getting the wrong answer....
a= 110
c= 140
Please reply showing what you did and what you got. Thank you! ;)
 
I'm sorry, but I don't understand. Do you know, or do you not know, how to find the value of b, given the values of a and c?


Please reply showing what you did and what you got. Thank you! ;)

Okay, I do understand how to find b, from the values of a and b.
I will update my original post.
 
Okay, I do understand how to find b, from the values of a and b.
I will update my original post.

You know how to find b given a and b? That's not hard is it!

From the Pythagorean Theorem which, as you say, asserts that \(\displaystyle c^2= a^2+ b^2\):

subtracting \(\displaystyle a^2\) from both sides: \(\displaystyle b^2= c^2- a^2\)
sugtracting ]tex]b^2[/tex] from both sides: \(\displaystyle a^2= c^2- b^2\)
 
Edit: So, here is what I have:
In future, please post your replies as replies, rather than as edits of previous portions of the conversation. Otherwise, things quickly become completely confused. :shock:

11022+b2=14022
12100+b2=19600
Actually, 1102^2 = 1214404. Did you maybe mean 110^2? Assuming so....

-12100 -12100
__ _____
✔️b2=✔️7500
I'm going to guess that you did two or three steps all at once, since of course 140^2 - 19600 does not equal sqrt[7500]. I think you meant the steps to be as follows:

. . . . .110^2 + b^2 = 140^2
. . . . .12,100 + b^2 = 19,600
. . . . .12,100 - 12,100 + b^2 = 19,600 - 12,100
. . . . .b^2 = 7,500
. . . . .b = +/- sqrt{7,500} = +/- sqrt{3*2,500}
. . . . .b = +/- sqrt{3*5*5*10*10}
. . . . .b = +/- sqrt{3} sqrt{5*5} sqrt{10*10}

...and then you continued the simplification and took only the positive square root. But how on earth did you (and all your friends) get that sqrt{2,500} somehow equalled 2,500?!?
 
You are good up to
\(\displaystyle \sqrt{b^2} = \sqrt{7500}\)
That is, b is the square root of 7500. However \(\displaystyle 2500 \sqrt{3}\) is not the square root of 7500. Now if that was a typo and you meant \(\displaystyle \sqrt{2500} \sqrt{3} = 50 \sqrt{3}\), then I don't see why the teacher would mark it wrong.
 
Guys, as Ishuda said, yes, I mistyped it, I got 50✔️3 instead of whatever I said before. As Stapel said, I did mean 110, not 1102. HallsOfIvy, I meant to say find b from c and a. Not from a and b.

Denis, basically what I said before, I mistyped it.

I guess I will just have to ask my teacher to recheck her math, if I did everything right (according to you guys and 25 other people). Thanks for your help.
 
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