Trigonometry is all about angles and sides of a right-angled triangle.

Recall that the side of the triangle opposite the right-angle is called the hypotenuse (Hyp). Further, note in the diagram that side is opposite (Opp) angle and side is adjacent (Adj) to angle .

Trigonometric Ratios

Reciprocal Ratios

To find the exact value of these ratios for angles 30^{o}, 45^{o} and 60^{o}, read the values from the following key triangles (for other values, use your calculator).

For 45^{o}:
Isosceles right triangle,
side length 1

For 30^{o} and 60^{o}:
Equilateral triangle,
side length 2

Solving problems

Trigonometric ratios can be used to solve problems involving right-angled triangles. In these cases, make sure you draw a diagram and label it carefully.

And do not forget about Pythagoras' Theorem:

(that is, "the square of the hypotenuse is equal to the sum of the
squares of the other two sides.")