Year 10 Interactive Maths - Second Edition

Naming the Sides of a Right-Angled Triangle

The side opposite the right angle is called the hypotenuse.  It is the largest side of a right-angled triangle.

If you stand at A in the triangle ABC, the side BC is opposite to you and the side AB is next to you.  We therefore say that BC is the opposite side to angle A and AB is the adjacent side to angle A.

Notation

Trigonometric Ratios

If you have trouble remembering the definitions, just remember SOH CAH TOA.

Using a Graphics Calculator

If you have a TI-83 graphics calculator, select Degree from the MODE menu and set Float to 4 to obtain the answers correct to 4 decimal places.  Press QUIT to return to the Home Screen and clear the screen if necessary.

If you are using another calculator, consult its instruction booklet or ask your teacher how you can set its Mode to 'Degree mode' and the decimal places display to 4 places.

Example 1

Evaluate the following to 4 decimal places:

Solution:

Recall that:

This is abbreviated as follows:

Example 2

Solution:

Note:

Key Terms

hypotenuse, opposite side, adjacent side, theta, trigonometric ratios, sine, sin, cosine, cos, tangent, tan, SOH, CAH, TOA, SOH CAH TOA, degrees, minutes, seconds