Trigonometry is the study in details of the relationship between the sides and the angles of triangles.

Types of triangles

1. Right angled triangle

A right angle triangle is a triangle in which one angle is equal to 90^o and the sum of all angles give 180^o. This means that the other two angles of a right angled triangle are equal to (180^o – 90^o) or 90.

This also means that in a right angled triangle, the 90^o angle must be the largest angle and the other two angles must be smaller than 90^o. The name of such angles is called the acute angles (angles which are larger than 0^o and smaller than 90^o). A right angle triangle can never contain an obtuse angle (an angle larger than 90^o and smaller than 180^o).

The two small angles in a right angled triangle add up to 90^o. Such angles are called complementary angles. If we know one of these angles we can calculate the other angle by subtracting the first from 90^o.

Since a + b = 90^o,

           b = 90^o – a

2. Isosceles right-angled triangles

The simplest right angled triangle to think about is the isosceles right angled triangle. In this triangle the two short sides are both equal. Since the sum of the smaller angles must be equal to 90^o, each small angle is then 45^o. In other words, isosceles right angled triangles are triangles with two equal sides with a total angle of 180^o.

3. Equilateral triangles

This is a type of triangle in which all the three sides are equal. An equilateral triangle can never be a right angle triangle, but when we divide an equilateral triangle into two halves it becomes two right angled triangles.

All equilateral triangles are similar triangles and the ratios of their sides are the same.