# Thread: Pythagoras equation for the hypotenuse of right angled triangles

1. ## Pythagoras equation for the hypotenuse of right angled triangles

I've got something which is really bugging me about Pythagoras, and I was wondering if you could help explain to me why the answer comes out as 21.26.

I have the equation shown here:

So I input (12,30) and (28,16) and the result should show as 21.26.

I am having trouble understanding how it has been worked out simply because whenever work it out, it seems to come out as 4.

So really my question is: How do I actually calculate using Pythagoras and these values above so that the answer comes out as 21.26?

Thanks if you can help.

2. Originally Posted by rushhour
I've got something which is really bugging me about Pythagoras, and I was wondering if you could help explain to me why the answer comes out as 21.26.

I have the equation shown here:

So I input (12,30) and (28,16) and the result should show as 21.26.

I am having trouble understanding how it has been worked out simply because whenever work it out, it seems to come out as 4.

So really my question is: How do I actually calculate using Pythagoras and these values above so that the answer comes out as 21.26?

Thanks if you can help.
The question is "How did you get 4?"
With X1= 12, X2= 28, X1- X2= 12- 28= -16 so $\displaystyle (X1- X2)^2= (-16)^2= 256$. With Y1= 30 and Y2= 16, Y1- Y2= 14 So $\displaystyle (Y1-Y2)^2= 14^2= 196$. So, according to the Pythagorean theorem, $\displaystyle h^2= 256+ 196= 452$. $\displaystyle h= \sqrt{452}= 21.26$ to two decimal places.

3. Originally Posted by HallsofIvy
The question is "How did you get 4?"
With X1= 12, X2= 28, X1- X2= 12- 28= -16 so $\displaystyle (X1- X2)^2= (-16)^2= 256$. With Y1= 30 and Y2= 16, Y1- Y2= 14 SO [tex](Y1-Y2)^2= 14^2= 196. So, according to the Pythagorean theorem, $\displaystyle h^2= 256+ 196= 452$. [tex]h= \sqrt{452}= 21.26 to two decimal places.
I am still having difficulty understanding it simply because the way you have worded it. It is slightly wrong from the equation i have which is $\displaystyle (X2 - X1)^2 + (Y2 - Y1)^2$ and the co-ordinates are (12,30) (28,16) I am now getting an answer of 21.63...........

4. Originally Posted by rushhour
I am still having difficulty understanding it simply because the way you have worded it. It is slightly wrong from the equation i have which is $\displaystyle (X2 - X1)^2 + (Y2 - Y1)^2$ and the co-ordinates are (12,30) (28,16) I am now getting an answer of 21.63...........

even with this its coming 21.26

5. Then tell me please, how are you getting the answer of 21.26? I have no idea! I keep getting 21.63 now, so its close, but not good enough. Please show me the exact steps in a step by step guide on how to come to this answer please.

6. Originally Posted by rushhour
I am still having difficulty understanding it simply because the way you have worded it. It is slightly wrong from the equation i have which is $\displaystyle (X2 - X1)^2 + (Y2 - Y1)^2$ and the co-ordinates are (12,30) (28,16) I am now getting an answer of 21.63...........
The order of the subscripts does not matter.

Originally Posted by rushhour
Then tell me please, how are you getting the answer of 21.26? I have no idea! I keep getting 21.63 now, so its close, but not good enough. Please show me the exact steps in a step by step guide on how to come to this answer please.

The solution given by HallsofIvy is complete and shows you exactly how to get 21.26. It cannot be said any plainer.

Until you show the complete working from which you got 21.63, it is impossible to say what mistake(s) you made in getting your answer of 21.63.

7. The way I am doing it is:

30 - 12 = 18
16 - 28 = -12

$\displaystyle 18^2$ = 324
$\displaystyle -12^2$ = 144

324 + 144 = 468

$\displaystyle \sqrt{468}$ = 21.63330765

and then the final answer is 21.63

This of course is not correct and I would like to know if my steps are wrong.

8. Originally Posted by rushhour
The way I am doing it is:

30 - 12 = 18 Mr F says: You are doing y1 - x1 here.
16 - 28 = -12 Mr F says: You are doing y2 - x2 here.

$\displaystyle 18^2$ = 324 Mr F says: You are doing (y1 - x1)^2 here.
$\displaystyle -12^2$ = 144 Mr F says: You are doing (y2 - x2)^2 here.

324 + 144 = 468

$\displaystyle \sqrt{468}$ = 21.63330765

and then the final answer is 21.63

This of course is not correct and I would like to know if my steps are wrong.
Compare what you have done with what the formula says to do.

9. Ok Thanks, I know where I have made my mistake now.