Working with right-angled triangles

Since mathematics in grade school, we’ve learned about Pythagoras. He was the Greek mathematician who came up with the relationship between the lengths of the sides of a right-angled triangle. This relationship is so important to vector mathematics that it is worth learning it off by heart. It states that for a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. Such a triangle is illustrated in Figure 8.5, with c indicating the hypotenuse:

Figure 8.5: A right-angled triangle

Given the right-angled triangle in Figure 8.5, the relationship between the hypotenuse and other sides can be written like this:

Important note

The hypotenuse is the side opposite the right angle.

Let’s work through the calculation of the hypotenuse using the triangle in Figure 8.6:

Figure 8.6: A right-angled triangle (with the...