90 Degree Angle Formula
Before learning the 90degree angle formula, let us recall a few things about a 90degree 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 rightangled triangle. It states that the sum of the squares of lengths of the adjacent sides of a right triangle is equal to the square of the length of the hypotenuse side. Further, this 90degree angle formula can be manipulated and 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 90degree angle is a right triangle. i.e.,
\(\text{Hypotenuse}^{2}=(\text{Adjacent Side})^{2}+(\text{Opposite Side})^{2}\)
Let us see the applications of the 90 degree angle formula in the following section.
Solved 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 rightangled 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,
\(\text{Hypotenuse}^{2}=(\text{Adjacent Side})^{2}+(\text{Opposite Side})^{2}\)
= \((5)^{2}+(12)^{2}\)
= (25+144)
\(\text{Hypotenuse}^{2}= (169)\)
Hypotenuse = \(\sqrt{169}\)
Hypotenuse = 13 cmAnswer: 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,
\(\text{Hypotenuse}^{2}=(\text{Adjacent Side})^{2}+(\text{Opposite Side})^{2}\)
\[ \begin{align}
8^2&= x^2 +x^2 \\
64 &= 2x^2 \\
x^2&= 32 \\
x &= 5.65
\end{align}\]Answer: We now have base = 5.65 units and height = 5.65 units.