[andyhaus1057]

There are 3 right triangles. The lengths of sides of each triangle are listed in the table below. The lengths of the triangles are represented by a and b. The letter c represents the length of the hypotenuse. How can I get the rest of the cells?


a b c a^2 b^2 c^2
Triangle 1 1 5 5.1 1 25 26

Triangle 2 2 4?

Triangle 3 3 2?

[Xoanan]

There are 3 right triangles. The lengths of sides of each triangle are listed in the table below. The lengths of the triangles are represented by a and b. The letter c represents the length of the hypotenuse. How can I get the rest of the cells?


a b c a^2 b^2 c^2
Triangle 1 1 5 5.1 1 25 26

Triangle 2 2 4 ? ? ? ?

Triangle 3 3 2 ? ? ? ?

Quick back ground info, not sure how comfortable you are...

C^2 (C "squared") will always be equal to A^2 + B^2. (this means "A times A" or "B times B"

So in triangle 1
A = 1
B = 5
C = 5.1

A^2 = A X A
or
1 X 1 = 1

B^2 = B X B
or 5 X 5 = 25

Since the law says that the square of the hypotenuses is equal to the "sums of the squares" of the other two sides, this must mean that:

C^2 = A^2 + B^2
or
C^2 = 1 + 25
C^2 = 26

So to find the value of C = you need to take the square root of 26 = which is roughly 5.1

Triangle #2
A = 2
B = 4
C = ?

So
A^2 = 2 X 2
or
A^2 = 4

B^2 = 4 X 4
or
B^2 = 16

Since C^2 MUST equal A^2 + B^2 then
C^2 = 4 + 16
or C^2 = 20

Then to find C take the square root of 20 = 4.47

Triangle #3
A = 3
B = 2
C = ?

A^2 = 3 X 3
or
A^2 = 9

B^2 = 2 X 2
or
B^2 = 4

therefore since C^2 MUST equal A^2 + B^2
C^2 = 9 + 4
or
C^2 = 13

To find C take the square root of 13, or 3.60

And there are your answers

The hardest part is figuring out the square root of the number. For ones that aren't nice and round you really need to use a calculator or "guess-and-check" methods.

If you have a scientific calculator look for the square root symbol. If you have a Windows computer, you can find "calculator" in the accessories group. Type in the number and click the "sqrt" button to get the square root.

If you need help remembering this, think of the 3,4,5 triangle.

A = 3
B = 4
C = 5

Proving the theory
A^2 = 9
B^2 = 16
C^2 = 25 (either 5X5=25 or 9+16=25)

Hope this helps