What is the length of a leg in a right-angled triangle if the hypotenuse is 17 cm?

The length of a leg in a right-angled triangle with a 17 cm hypotenuse depends on the other leg's length.

In a right-angled triangle, the relationship between the sides is given by Pythagoras' Theorem, which states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. Mathematically, this is written as \(a^2 + b^2 = c^2\), where \(c\) is the hypotenuse, and \(a\) and \(b\) are the other two sides.

Given that the hypotenuse \(c\) is 17 cm, we can use this theorem to find the length of one leg if we know the length of the other leg. For example, if one leg \(a\) is 8 cm, we can find the other leg \(b\) by rearranging the formula to \(b^2 = c^2 - a^2\). Substituting the known values, we get \(b^2 = 17^2 - 8^2 = 289 - 64 = 225\). Taking the square root of both sides, we find \(b = \sqrt{225} = 15\) cm.

If we don't know the length of either leg, we can't determine the exact length of a leg just from the hypotenuse alone. However, if you have one leg's length, you can always use Pythagoras' Theorem to find the other. This theorem is a fundamental part of GCSE Maths and is very useful for solving problems involving right-angled triangles.