Lesson 9: Right Triangles and the Pythagorean Theorem

So far, we have covered a lot of physics so today, I thought we would look into a little math, more specifically, trigonometry. You might be asking why we are covering this or even why triangles are so important in the first place. The reason is, most geometric shapes can be broken down into numerous triangles for easier calculations which makes everyone's life a little easier. Think of a hexagon, square, octagon. These shapes occur frequently and can be broken down into individual triangles. Additionally, a lot of higher math and physics require vector analysis which requires a substantial amount of trigonometry.

The most basic type of triangle is called the right triangle. Its name states that the triangle contains one right angle which is a 90 degree angle. These types of triangles are the easiest to work with due to the fact that they correlate with simple formulas. Today we will discuss the Pythagorean Theorem. This is an equation which will give us the length of a third side when the lengths of the other two are inserted.

The formula is C^2 = A^2+B^2. C is the length of the hypotenuse of the triangle, which is the longest side, and A and B are the lengths of the other two sides. In order to use this formula, we would plug in the lengths of the two sides that we know and solve for the third.

Lets go through an example so you can get the hang of how this formula works. Let's say we have a triangle with two smaller sides with the lengths of 3 meters and 4 meters. We would plug these values in to get. C^2=(3)^2+(4)^2. We then have 9+16 which is equal to 25. We still have C^2 and we want C so we would take the square root of both sides to get C=5. Now we know the lengths of all of the sides of the triangle in question.

This theorem is extremely useful, and can be applied across a wide variety of applications such as finding the length of diagonal poles needed to make a tent or finding if a square is truly square (if both diagonals inside the square are equal in length).

So, make up a few measurements and try this formula out for yourself. It is relatively simple so you should get the hang of it quickly. If you have any questions just leave a comment and I will reply promptly.

For more information, check out http://en.wikipedia.org/wiki/Pythagorean_theorem