Last updated on August 5th, 2025
In mathematics, the hypotenuse is the longest side of a right triangle, opposite the right angle. In this topic, we will learn the formula to calculate the hypotenuse using the Pythagorean theorem.
The hypotenuse is calculated in a right triangle using the Pythagorean theorem. Let’s learn how to calculate the hypotenuse using different scenarios.
The hypotenuse of a right triangle can be calculated using the Pythagorean theorem, which states that the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b):
Hypotenuse formula: ( c = √{a2 + b2})
The hypotenuse formula is crucial in geometry and real-life applications.
Here are some important uses of the hypotenuse formula:
Many students find math formulas tricky and confusing.
Here are some tips and tricks to master the hypotenuse formula:
The hypotenuse formula plays a significant role in real-life scenarios.
Here are some applications of the hypotenuse formula:
Students often make errors when calculating the hypotenuse. Here are some mistakes and ways to avoid them:
Calculate the hypotenuse of a right triangle with sides 3 and 4.
The hypotenuse is 5.
Using the formula ( c = √{a2 + b2}) where a = 3, b = 4:
( c = √{32 + 42})
=√{9 + 16}
= √{25}
= 5
Find the hypotenuse if one side is 5 and the other is 12.
The hypotenuse is 13.
Using the formula ( c = √{a2 + b2}), where a = 5, b = 12:
( c = √{52 + 122})
= √{25 + 144}
= √{169}
= 13
A triangle has a hypotenuse of 10 and one side of 6. Find the other side.
The other side is 8.
Using the formula ( c2 = a2 + b2 ), where c = 10 and a = 6:
( 102 = 62 + b2 )
( 100 = 36 + b2 )
( b2 = 64 )
( b = √{64} = 8 ).
Find the length of the hypotenuse when the sides are 8 and 15.
The hypotenuse is 17.
Using the formula ( c = √{a2 + b2}) , where a = 8, b = 15:
( c = √{82 + 152})
= √{64 + 225}
= √{289} = 17 ).
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
: He loves to play the quiz with kids through algebra to make kids love it.