Pythagorean theorem:
x^2 + 6^2 = 15^2
Solve for x.
x^2 + 6^2 = 15^2
Solve for x.
In this case, the ladder acts as the hypotenuse, while the distance from the base of the ladder to the house represents one of the shorter sides.
Let's call the height on the house that the ladder reaches "h." According to the problem, the base of the ladder is 6 feet away from the house, so the other shorter side of the triangle would also be 6 feet.
Using the Pythagorean Theorem, we can solve for "h":
h^2 = 15^2 - 6^2
h^2 = 225 - 36
h^2 = 189
To find the value of h, we take the square root of both sides:
h = √189
h ≈ 13.73
Therefore, the ladder reaches a height of approximately 13.73 feet on the house.
Using the Pythagorean theorem:
(ladder)^2 = (base)^2 + (height)^2
Substituting the given values:
(15 feet)^2 = (6 feet)^2 + (height)^2
225 square feet = 36 square feet + (height)^2
Subtracting 36 square feet from both sides:
189 square feet = (height)^2
To find the height, take the square root of both sides:
√189 square feet = √(height)^2
13.74 feet = height
Therefore, the ladder goes approximately 13.74 feet high on the house.