What is the adjacent side in trigonometry?

The adjacent side in trigonometry is the side next to the angle of interest in a right-angled triangle.

In trigonometry, particularly when dealing with right-angled triangles, the sides of the triangle are given specific names relative to a chosen angle. The adjacent side is the one that forms the angle of interest along with the hypotenuse, which is the longest side of the triangle. It is important to note that the adjacent side is not the hypotenuse itself, but the other side that touches the angle.

For example, if you have a right-angled triangle and you are focusing on one of the non-right angles, the side that is directly next to this angle (but not the hypotenuse) is called the adjacent side. The other side that is opposite to this angle is called the opposite side. Understanding which side is adjacent is crucial when using trigonometric ratios such as cosine, which is defined as the ratio of the length of the adjacent side to the length of the hypotenuse (cosine = adjacent/hypotenuse).

Knowing how to identify the adjacent side helps in solving various problems involving right-angled triangles, such as finding missing side lengths or angles. It is a fundamental concept that underpins much of trigonometry, so getting comfortable with identifying and using the adjacent side is essential for success in GCSE Maths.