Cosine Ratio (CAH)

The cosine of an angle in a right triangle tells you how much of the hypotenuse lies along the side next to the angle. It works because, for a fixed angle, all similar right triangles have the same side-length ratio, so the adjacent-to-hypotenuse comparison depends only on the angle, not the triangle’s size. Cosine is one of the three basic trigonometric ratios used to connect angles with lengths.

Use this formula when you know a right triangle’s angle and the hypotenuse, or when you need to find an adjacent side. It is also useful in geometry, navigation, physics, and any problem involving angles and distances.

• Using cosine with the wrong sides, such as opposite instead of adjacent
• Forgetting that the hypotenuse is always the longest side and is opposite the right angle
• Entering the angle in the wrong unit or using the wrong cosine value from a calculator