Q. What is Common Triangles?

Ans.

Some triangles appear more commonly than others. You will come across two triangles repeatedly as you learn more about trigonometry.

The most common isosceles triangle found in trigonometry is constructed with the two equal sides both of length 1 with an interior right angle.

We can use the Pythagorean Theorem to determine the length of the missing side.

1² + 1² = x²
1 + 1 = x²
2 = x²

√2 = √x²

√2 = x

The length of the missing side is

What are the missing angles?

Recall from geometry that if a triangle has two sides of equal length, the angles opposite those sides must be equal to each other.

Since the sum of the interior angles of a triangle must equal 180^o , we have:

90^o + 2x = 180^o
2x = 180^o - 90^o
2x = 90^o
x = 45^o

The missing angles are 45^o , or radians. This is because