In a right-angled triangle, the leg and hypotenuse are 12 and 20, respectively. Find the other leg of this triangle.

Let’s designate the second leg of a right-angled triangle as x.
Remember the Pythagorean theorem: the sum of the squares of the legs is equal to the square of the hypotenuse. That is, in our case:
x ^ 2 + 12 ^ 2 = 20 ^ 2
We derive from this equation x ^ 2:
x ^ 2 = 20 ^ 2 – 12 ^ 2
x ^ 2 = 400 – 144
x ^ 2 = 256
x = √256 (sqrt – under the root)
x = 16
Answer: the other leg of a right-angled triangle is 16.