Final answer:
The length of the long leg of the given 30-60 right triangle with a short side of 5 units is 10 units.
Step-by-step explanation:
In a 30-60 right triangle with a short side of 5 units, we can use the Pythagorean theorem to find the length of the long leg. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Let's label the short side as 'a', the long leg as 'b', and the hypotenuse as 'c'. Since we know 'a' is 5, we can use the formula:
c = √(a^2 + b^2)
In this case, since it's a 30-60 right triangle, the long leg will be double the length of the short side. Therefore, the long leg would be 10 units.