What is Pythagoras's theorem?

Pythagoras's theorem is used to calculate the lengths of the sides of right-angled triangles. The theorem can be used to find the length of the third side of a right-angled triangle, as long as the lengths of the other two sides have been provided. The theorem is: a2 + b2 = c2, where c is the length of the hypotenuse, or longest side. The hypotenuse always lies opposite to the right-angle, while a and b are the two sides which form the right-angle. It doesn't matter which of these two sides is a and which is b, as long as you are consistent in sums. Take, for example, the simplest question: a right-angled triangle has two sides of length 3 and 4 - these sides are adjacent to the right-angle. What is the length of the hypotenuse? Sides a and b are therefore 3 and 4. a2 + b2 = c2   so   32+4= c2     so   25 = c2   so  c = 5. The formula can also be rearranged. For example, if you are given the hypotenuse and one other side's length, you can still calculate the third side's length: A right-angled triangle has a hypotenuse of length 13 and another side of length 12. What is the length of the third side?  We know that c = 13 and another side - let's call it b - is 12. First, rearrange the formula to put it in terms of a: a2 + b2 = c2    becomes    a2  = c- b2 So a2 = 132 - 122    so  a2 = 169-144    so  a2 = 25  so  a = 5.

SJ
Answered by Samuel J. Maths tutor

3620 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

How do I expand (2x+5)(9x-2)?


How do I sketch a quadratic function on graph paper?


The equation of the line L1 is y=3x–2. The equation of the line L2 is 3y–9x+5=0. Show that these two lines are parallel.


Write the equation x^2 + 6x - 40 = 0 in the form (x + a)^2 - b = 0 and then solve for x


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning