Finding the Values of a and b in the Pythagorean Theorem

[eNathan]

The pythagorean theorum states that $a^2+b^2=c^2$. 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 don't 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.

Thanks in advance :tongue2:

 

[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.

 

[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.

 

[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= $\sqrt{c^2- a^2}$.

 

[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.

 

[Gokul43201]

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.

That's what trigonometry is for.

b = c cos40
a = c sin40

 

[eNathan]

That's what trigonometry is for.

b = c cos40
a = c sin40

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

 

[HallsofIvy]

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