Hypotenuse Formula

About Hypotenuse Formula

In a right-angled triangle, the hypotenuse formula is used to compute the longest side, which is termed the hypotenuse. In a right triangle, the hypotenuse is always the side opposite the right angle. To get the hypotenuse and consequently the hypotenuse formula, we use Pythagoras' theorem.

What Is Hypotenuse Formula?

The Pythagoras theorem or hypotenuse formula states that the square of the hypotenuse equals the sum of the squares of the other two sides (legs).

  • Pythagoras Theorem: a2 + b2 = c2
  • Here, c is hypotenuse, a is height (a leg) and b is base (a leg)
  • From Pythagoras theorem,(hypotenuse)2= (base)2+ (height)2
  • If we take square root on both sides, we get the formula of the hypotenuse.
  • Hypotenuse formula = √((base)2 + (height)2) (or) c = √(a2+ b2)

Let us solve some interesting problems using the hypotenuse formula.

Solved example of Hypotenuse Formula

Example: Solve for the longest side of the supplied bread slice that is similar to a right-angle triangle using the hypotenuse formula. It has a 13-unit height and a 5-unit base.

  • Sol:
  • To findout the longest side (hypotenuse) of the bread slice.
  • Its height = 13 units.
  • Its base = 5 units.
  • By using the hypotenuse formula,
  • hypotenuse formula = √ ((base)2+ (height2)
  • = √(52+132)
  • = √25+169
  • = √194
  • = 13.98

Maths Formulas prepared by HT experts are listed on the main page.

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Hypotenuse Formula

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