Concept preview

What you will be able to do

1. 01Identify the hypotenuse and the opposite and adjacent sides relative to an angle.
2. 02Use SOH-CAH-TOA to write the sine, cosine, and tangent of an angle.
3. 03Find an unknown side given an angle and one side.
4. 04Find an unknown angle from two sides using inverse trigonometric functions.
5. 05Solve angle-of-elevation and angle-of-depression problems.

Pythagoras is powerful, but it only ever relates the three sides of a right triangle to one another — it is completely silent about the angles. Trigonometry fills that gap by making a bridge between an angle and the ratio of two of the sides. That bridge is astonishingly useful: as soon as you know one acute angle and just one side of a right triangle, trigonometry lets you recover every other side and angle. It is the mathematics behind measuring the height of a mountain, plotting a ship's course, and resolving forces in physics — anywhere a distance is hard to reach but an angle is easy to measure.