Introduction :

In mathematics, the special triangles are in the topic trigonometry. In trigonometry, the special triangles are having three angles. In trigonometry, special triangles are classified into two
types. In trigonometry, the classification of the special triangles is based on their angles only. The names of the special triangles are given as isosceles right triangles and scalene right
triangles. The detailed explanation for the special triangles is given below.

Special Triangles Trigonometry – Types:

Isosceles right triangles

The diagram for these special triangles is given below,

special triangle 1

An isosceles right triangle is one of the special right triangles in trigonometry. The angle measurements of these special triangles are in 45-45-90. Where, 45-45-90 is another name for
these special triangles. The ratio for the sides of these special triangles is (1, 1, v (2)).

Scalene right triangles:

The diagram for these special triangles is given below,

special triangle 2

Scalene Right Triangles is one of the special right triangles in trigonometry. The angle measurements of these special triangles are in 30-60-90. Where, 30-60-90 is another name for these
special triangles. The ratio for the sides of these special triangles is (1, v (3), 2).

Formula to calculate the sides of the special triangles is,

c2 = a2 + b2

Special Triangles Trigonometry – Examples:

Example 1: Check whether it is special triangle or not from given data a = 4, b = 4v (3)?

Solution:

Formula to calculate the sides of the special triangles is,

c2 = a2 + b2

c2 = 42 + 4v (3) 2

c2 = 16 + 48

c2 = 64

c = v (64)

c = 8 = 2(4)

Thus, it is in the ratio (1, v (3), 2)

Yes, it is special triangle and it is a scalene right triangles.

Special triangles trigonometry– Practice problem:

Problem 1: Check whether it is special triangle or not from given data a = 6, b = 6?

Answer is given below:

Yes, it is special triangle and it is isosceles right triangles.

Problem 2: Check whether it is special triangle or not from given data a = 9, b = 7?

Answer is given below:

No, it is not a special triangle.