Final answer:
Using the Pythagorean theorem, we find that James' ladder, which forms a right-angle triangle with the ground and the house, is 13 feet long.
Step-by-step explanation:
To determine how long James' ladder is, given that it is 12 feet from the ground and the base of the ladder is 5 feet from the side of the house, we can use the Pythagorean theorem. The ladder, the ground, and the side of the house form a right-angle triangle.
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
If we let c represent the length of the ladder (the hypotenuse), a represent the distance from the house (5 feet), and b represent the height from the ground (12 feet), the equation is:
c² = a² + b²
Plugging in the known values, we have:
c² = 5² + 12²
c² = 25 + 144
c² = 169
Therefore, c = √169
c = 13
The ladder is 13 feet long.