90 Degree Angle Formula

Before learning the 90-degree angle formula, let us recall a few things about a 90-degree angle. When the angle between two rays is equal to 90 degrees, then the angle formed is called a right angle. Pythagoras theorem is used in a right-angled triangle. It states that the sum of the squares of lengths of the adjacent and opposite sides of a right triangle is equal to the square of the length of the hypotenuse side. Further, this 90-degree angle formula can be used to determine the right angle.

What Is a 90 Degree Angle Formula?

The 90 degree angle formula is nothing but the Pythagoras theorem of a right triangle as the triangle with a 90-degree angle is a right triangle. i.e.,

 Hypotenuse²=(Adjacent Side)² + (Opposite Side)²

Let us see the applications of the 90 degree angle formula in the following section. 

Examples Using 90 Degree Angle Formula

Example 1: Find the length of the hypotenuse of a triangle when the length of the other sides of the right-angled triangle is 5 cm and 12 cm.

Solution:

To find: the length of the hypotenuse of a triangle.          

Given parameters are,
The sides of the right triangles are 5 cm and 12 cm.

Using the 90 degree angle formula,

Hypotenuse²=(Adjacent Side)² + (Opposite Side)²

=  (5)² + (12)²

= (25+144)

Hypotenuse² = (169)
Hypotenuse = √169
Hypotenuse = 13 cm          

Answer: The length of the hypotenuse of a triangle is 13 cm.

Example 2: The hypotenuse of a right isosceles triangle is 8 units. Find the measure of the other two sides.

Solution: 

To find: The measure of the other two sides

The hypotenuse of a right isosceles triangle = 8 units

Using the 90 degree angle formula,

Hypotenuse²=(Adjacent Side)² + (Opposite Side)²

8² = x² + x²

64 = 2x²

x = 5.65

Answer: We now have base = 5.65 units and height = 5.65 units.