Naming the sides of a right-angled triangle

Trigonometry – Right Angled Triangles

By the end of this lesson you will be able to identify and calculate the following:1. Hypotenuse, Opposite Side, and, Adjacent Side2. The Tangent Ratio

Naming the sides of a right-angled triangle:

In trigonometry, angles are often named using letters of the Greek alphabet, such as: θ (pronounced as ‘theta’), α (pronounced ‘alpha’), β (‘beta’), γ (’gamma’) and others.

Naming the sides of a right-angled triangle:

The longest side of a right-angled triangle is called the hypotenuse. It is always opposite the right

The other two sides of a right-angled triangle are named according to their position with respect to a specific angle.

The side which is opposite to the angle is named opposite

The side next to the angle is named adjacent.

Naming the sides of a right-angled triangle:

In the diagram the longest side, opposite the right angle, is side AB.

So AB is the hypotenuse.

Side BC is opposite angle θ and side AC is next to angle θ.

So, in relation to this angle, side BC is ‘opposite’ and side AC is ‘adjacent’.

Worked Example:

Worked Example

The Tangent Ratio:

In trigonometry, the ratios of sides in right-angled triangles are of particular importance.

These ratios have special names.

In any right-angled triangle, the ratio of the opposite side to the adjacent side is called the tangent ratio.

Worked Example

Worked Example

From the previous worked example we can conclude that: regardless of size any right-angled triangle

where one of the angles is equal to 30°

the ratio of the side opposite that angle to the side adjacent to that angle (the tangent ratio) will always be 0.58.