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# 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.,

Hypotenuse^{2}=(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,

Hypotenuse^{2}=(Adjacent Side)^{2 }+ (Opposite Side)^{2}

= (5)^{2 }+ (12)^{2}

= (25+144)

Hypotenuse^{2 }= (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,

Hypotenuse^{2}=(Adjacent Side)^{2 }+ (Opposite Side)^{2}

8^{2 }= x^{2} + x^{2}

64 = 2x^{2}

x = 5.65

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

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