## Hypotenuse

Inside a right-angled triangle, the hypotenuse equation is being used to compute the longest side, which is known as the hypotenuse. In a right triangle, the hypotenuse is the side opposing the right angle. To get the hypotenuse & consequently the hypotenuse formula, you use Pythagoras’ theorem.

## What is Hypotenuse Formula?

The Pythagorean theorem states that the square of that hypotenuse equals the sum of squares of the other two sides. Let us look at the Pythagorean theorem to see how the hypotenuse formula is derived.

Here,

c =stands for hypotenuse.

a = the height

b = base

a^{2} + b^{2} = c^{2}

The hypotenuse formula is obtained by taking the square root along both sides.

Hypotenuse equation = (base)^{2 }+ (height)^{2 }= hypotenuse^{2} = (a^{2} + b^{2}) = c^{2}

## Solved Examples

**Q. Solve again for the longest side of a provided bread slice, which is identical to a right – angled triangle, using hypotenuse formula. It has a height of 13 units and then a width of 5 units. **

A. To locate: the bread slice’s longest side (hypotenuse).

It has a height of 13 units.

It has a base of 5 units.

The hypotenuse formula is used to calculate

(base)^{2} + (height)^{2 }= hypotenuse^{2}

= √(25+169) = 13.98

The longest length of a bread slice is 13.928 units.

**Q. A right triangle’s hypotenuse is 5 units long. It has a three-unit basis. Using the hypotenuse formula, determine its height. **

A. The length of a correct triangle must be determined.

Let us suppose it is ‘h’.

Its hypotenuse is 5 units long.

It has a base of 3 units.

Hypotenuse^{2} =(base)^{2} + (height)^{2} is the hypotenuse formula.

25 -9 = h^{2}

25−9 = h^{2}

16 = h^{2}

h = 4

The right triangle’s height is 4 units.

**Q. Solve again for the longest side of the supplied bread slices that really is similar toward a right – angled triangle that uses the hypotenuse formula. It has a height of 14 units and a base of 8 units. **

A. To locate: the bread slice’s longest side (hypotenuse).

It has a height of 14 units.

It has a base of 8 units.

The hypotenuse formula is used to calculate

= √64+196 = 16.124

The lengthiest side of a bread piece is 16.124 units.