30-60-90 Formulas

There are many types of triangles. Acute, Obtuse, Isosceles, Equilateral triangles. Out of these different triangles, few of them are special. When we say special, it means the sides and angles which are predictable and consistent.

Thirty sixty ninety triangle

Out of all the other shortcuts, 30-60-90 is indeed a special triangle.

What is a 30-60-90 Triangle?

It is a triangle where the angles are always 30, 60 and 90. As one angle is 90, so this triangle is always a right triangle. As explained above that it’s a special triangle so it has values of lengths values and angles values.

The basic 30-60-90 triangle ratio is:

The side opposite the 30° angle

x

The side opposite the 60° angle

X * √3

The side opposite the 90° angle

2x

Examples of 30 – 60 -90 rules

Example 1

Solution:

As it is a right triangle in which the hypotenuse is always the double of one of the sides of the triangle. That’s why it is called a 30-60-90 triangle where smaller angle will be 30. The longer side is always opposite to 600 measures 6√3.

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Practise This Question

If a=^i+^j+2^k, b=2^i^j^k then c=2^i+^j+3^k, then the angle between 2a-c and a+b is: