Right Angle Trigonometry

We can use trig to slam-dunk the opposing team in basketball or do real damage to a tennis challenger in a singles match. We can figure out the ideal distance between the basket and the foul line by doing a trig calculation. Hint: the distance is one side of a triangle, and if we do the Pythagorean thing—more on that later—we can figure it all out.

Behold your mathematical journey:

Right angles → Trigonometry → Trigonometric Functions → Calculus → Physics → The Meaning of Life

Okay, understanding right angles might not help us understand the meaning of life. Knowing about right triangles does help us understand the physical world, though.

Trigonometric functions (also called trig functions by the all cool kids) are all about the angles. What did you expect—Benjamins? With trig, we can study the relationship between these right triangles and the sides that sit opposite to them. (Warning: it's hot and heavy).

Let's get this trigonometry thing started.

Take a peek at ∆ABC:

Look! It's a triangle with legs! Okay, maybe it's not wearing jeans. But it still has legs. Angle C is the right angle, and side c is the hypotenuse.

Sides a and b are the legs.

Remember from geometry that the side opposite an angle gets the same name, just a lower case letter.

This means side a is opposite angle A and side b is opposite angle B. The hypotenuse, usually designated by letter c, is always opposite the right angle C.