# The pythagorean theorum

1. Jan 25, 2005

### eNathan

The pythagorean theorum states that [Itex]a^2+b^2=c^2[/Itex]. So if you know the value of c^2, or just c, how do you get the vales of a and b, assuming that those arethe legs of a right triangle? And I dont mean the sum of a and b, I mean them seperatly. This has to mathamaticly be posible because you can draw a driagram on paper to do this.

2. Jan 25, 2005

### hypermorphism

You need to know at least one angle other than the right angle, in which case you will know all three angles. Then you can use the definitions of the trigonometric functions to get each side.

3. Jan 25, 2005

### NeutronStar

Yes, you either need to know c and a, or c and b, or c and some angle in addition to the 90 degree angle.

Don't forget, the Pythagorean Theorem only works for right triangles.

For any given value of c there can be infinitely many combinations of values for a and b depending on the angles of the right triangle. But once you chose a value for a or b, then the other is fixed. Keep in mind also that both a and b need to be less than c in all cases.

Alternatively if you know the angles of the right triangle then both a and b are also fixed.

4. Jan 25, 2005

### HallsofIvy

"This has to mathamaticly be posible because you can draw a driagram on paper to do this."
No, that's not true.
Given ONLY c, you can draw an infinite number right triangles with that hypotenus- Immagine the hypotenuse pivoting on a point with a "weight" hanging from the other end. As you swing the hypotenuse upward, the horizontal length decreases while the vertical length increases.

Given a hypotenuse length c, a can be any number from 0 to c and then
b= $\sqrt{c^2- a^2}$.

5. Jan 26, 2005

### eNathan

Ewo

What I mean is that if you know the hypotenuse, and the angle at which one of the legs IE A and B occur, you can get the value of both of them. :yuck:

Let me give this example. you have a hypotenuse of 2 meters, and the angle at which B occurs is 40, or something like that, you can draw a diagram on paper to figure out the length of a and b.

Last edited: Jan 26, 2005
6. Jan 26, 2005

### Gokul43201

Staff Emeritus
That's what trigonometry is for.

b = c cos40
a = c sin40

7. Jan 26, 2005

### eNathan

Does that mean
b = c*cos(40)
a = c*sin(40)

8. Jan 26, 2005

### HallsofIvy

Yes, that's what he wrote, that's what he meant