a 15 foot lader is leaned against a house. the base of the ladder is 6 feet from the house. How high on the house does the ladder go
Pythagorean theorem:
x^2 + 6^2 = 15^2
Solve for x.
To find out how high on the house the ladder goes, we can use the Pythagorean Theorem. The theorem states that in a right-angled triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse.
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.
To determine how high on the house the ladder goes, you can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the ladder is the hypotenuse, and the base of the ladder and the height on the house are the other two sides of the right triangle.
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.