Given a right-angled triangle with legs 5 and 3. Find the hypotenuse.

To find the lengths of the sides in a right-angled triangle, use the Pythagorean theorem. The Pythagorean theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs:
c ^ 2 = a ^ 2 + b ^ 2,
where a and b are legs, c is hypotenuse.
If, according to the condition, leg a = 5 conventional units, leg b = 3 conventional units, then the hypotenuse c is equal to:
c ^ 2 = 5 ^ 2 + 3 ^ 2;
c ^ 2 = 25 + 9;
c ^ 2 = 34;
c = √34 conventional units.
Answer: the hypotenuse is equal to √34 conventional units.