In a rectangular triangle, one of the legs is 7 cm, and the hypotenuse is 13, find the other leg.

In order to find what the second leg of the right-angled triangle specified in the task is equal to, we need the Pythagorean theorem.
According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of two legs.
That is, c² = a² + b², where a and b are the legs of the triangle, and c is its hypotenuse.
Now we write down the formula and find the second leg of the triangle.
c² = a² + b².
a² = c² – b².
a² = 13² – 7².
a² = 169 – 49.
a² = 120.
a = √120.
a = √4 × √30.
a = 2√30 (cm).
Answer: a = 2√30 cm.