ill start with the last part first.

if you have something like a=10 b=? and c=26 (and you know is a right triangle) than express it in an equation

now its 10^2 + b^2 = 26^2 or

100 + b^2 = 676

now subtract 100 using algeba and square root both sides to find b.

b^2 = 576

b= 24

now next…

16^2 + 30^2 = 34^2

256 + 900 = 1156

1156 = 1156

because you did the pythag theorum you know it works.

To see if it is a pythag triple

you reduce all of the original numbers. in this case you reduce by two.

16, 30, 34 becomes

8, 15, 17

now you know this is a pythgorean triple because it is always true

for reference, the following are pythagorean triples when reduced:

( 3, 4, 5) ( 5, 12, 13) ( 7, 24, 25) ( 8, 15, 17)

( 9, 40, 41) (11, 60, 61) (12, 35, 37) (13, 84, 85)

(16, 63, 65) (20, 21, 29) (28, 45, 53) (33, 56, 65)

(36, 77, 85) (39, 80, 89) (48, 55, 73) (65, 72, 97)

Since 16, 30, and 34 work in the equation, it is a Pythagorean triple. This means that it can also be the sides of a right triangle.

To find the missing side in the equation. Plug in the 2 numbers you have and solve it as a regular equation.

Hope this helped, hon. Good luck.

Then you take that answer and square root it, and then you have the missing letter.

Example: 9+B^2=25

B^2=16

B=4

Part 2: I think that it will answer whether or not they are Pythagorean triples. Again, I THINK. And to find if it makes a Pythagorean triple, you add together the squares of 16, and 30, and you see if they equal the square of 34. If so, then they are a Pythagorean triple.

A Pythagorean triple is one in which all the numbers are whole numbers like 3,4,5 is a triple because 3^2 + 4^2 = 5^2.

To find the hypotenuse given the legs,you ADD. When you have the hypotenuse and are looking for a leg you SUBTRACT.

10^2 + b^2 = 26^2

100 + b^2 = 676

b^2 = 576

√b^2 = √576

b = 24