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Way way back many centuries ago, Pythagoras and his students stated the following theorem, which is still used today.
In any right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Thus in the above right-angled triangle, a2 + b2 = c2
Remember that the triangle must be right-angled and that the hypotenuse is always the longest side and the one opposite the right angle.
Example
Use Pythagoras' Theorem to calculate the length of the hypotenuse, c, in the following right-angled triangle. Give your answer to 3 significant figures.
Answer
By Pythagoras' Theorem,
c2 = 32 + 82
c2 = 9 + 64
c2 = 73
c = √73
c = 8.54 (to 3 s.f.)
