In a right-angled triangle, the leg and hypotenuse are 16 and 34, respectively. Find the other leg of this triangle.

According to the Pythagorean theorem, in a right-angled triangle, the sum of the squares of the legs is equal to the square of the hypotenuse:
c² = a² + b² where c is the hypotenuse, a and b are the legs of a right-angled triangle.
From here we will find expressions for determining the leg:
a² = c² – b²
a = √ (c² – b²) = √ (34² – 16²) = √ (1156 – 256) = √900 = 30 (second leg).
Answer: the second leg is 30.