What Is the Adjacent?

What Is the Adjacent?

The adjacent is the shorter side next to a given angle of a right triangle (also called a right-angled triangle).

If we choose one of the angles of the right triangle that is not the right angle then the adjacent is the shorter side next to that angle.

The image below shows what we mean by the angle (labelled θ) and the adjacent:

The Adjacent and Trigonometry

Trigonometry relates an angle within a right triangle to the lengths of its three sides (called the hypotenuse, adjacent and opposite).

The image below shows what we mean by an angle (labelled θ) and the three sides (the hypotenuse, adjacent and opposite).

  • The cosine function relates the angle in a right triangle to the ratio of the length of the adjacent side to the length of the hypotenuse:

  • The tangent function relates the angle in a right triangle to the ratio of the length of the opposite side to the length of the adjacent:

The Adjacent and Pythagoras' Theorem

Pythagoras' theorem concerns the relationship between the lengths of the three sides of the right triangle.

Pythagoras' theorem (or the Pythagorean theorem) states that:

The square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.

It is easier to remember Pythagoras' theorem as a formula:

a2 + b2 = c2

This formula can be rearranged to show the length of the adjacent in terms of the other two sides:

In the formula, a is the length of the adjacent, b is the length of the opposite and c is the length of the hypotenuse. The image below shows what we mean:

See Also

What is the cosine function? What is the tangent function? What is Pythagoras' theorem? Finding a shorter side using Pythagoras' theorem Learn more about Pythagoras' theory ( interactive widget) Learn more about the sine function in trigonometry ( interactive widget) Learn more about the cosine function in trigonometry ( interactive widget)