The acute angles of a right triangle are complementary.

Given

Right triangle ABC

 

Prove

Proof

1: - Given
2: -  In a triangle, the sum of the measures of the interior angles is 180°

3: - substitute 1 in 2

4: - From 3

Definitions of Sin, Cosine and Tangent

A right triangle consists of one angle of 90^oand two acute angles. Each acute angle of a right triangle has the properties of sine, cosine and tangent. The sine, cosine and tangent of an acute angle of a right triangle are ratios of two of the three sides of the right triangle.

right triangle

The sine of the angle is the ratio of the length of the side opposite the angle divided by the length of the hypotenuse.

 

  

The cosine of the angle is the ratio of the length of the side adjacent to the angle divided by the length of the hypotenuse.

  

The tangent of the angle is the ratio of the length of the side opposite the angle divided by the length of side adjacent to the angle.