*Put simply trigonometry is the study of triangles and their properties, such as their angles and lengths and how these are related. Central to trigonometry is the ***right angled triangle. **It is very important to know and understand the different properties of right angled triangles. Some of these you may have already encountered such as **Pythagoras Theorem **and area of triangles. In this chapter you will be working with **trigonometric ratios**, these are commonly referred to as sin, cos and tan.

## Trigonometric ratios

Trigonometric ratios relate the sides of a right angle triangle to one of its angles, they can be used to find missing side lengths and angles in right-angled triangles. In this section we label a right-angled triangle, with angle θ as follows:

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Here the side opposite the angle θ is the ‘opposite side’ and the side next to the angle θ is the ‘adjacent side’. It is a common mistake to confuse these two sides, or even confuse them with the ‘hypotenuse’ which is the longest side of a right-angled triangle. Make sure you carefully identify each of the opposite, adjacent and hypotenuse sides for a given angle before using the trigonometric ratios.

For an angle θ in a right-angled triangle, the trigonometric ratios are:

sine(θ) = length of opposite side/length of hypotenuse

cosine(θ) = length of adjacent side/length of hypotenuse

tangent(θ) = length of opposite side/length of hypotenuse

These ratios will appear in abbreviated form:

sin(θ) = Opposite(O) / Hypotenuse(H)

cos(θ) = Adjacent(A) / Hypotenuse(H)

tan(θ) = Opposite(O) / Adjacent(A)

A useful acronym for remembering these ratios is **SOH-CAH-TOA**, here **S** represents sine which is equal to opposite **O **divided by hypotenuse **H **(this makes SOH and the next parts correspond to cos and tan respectively).

**See also:**

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