a 16-foot ladder is leaning against a house and is 2 feet away from the foundation of the house. How high up will the ladder reach?
2^2 + h^2 = 16^2
4 + h^2 = 256
h^2 = 252
h = 15.87 ft
By the way that ladder is dangerously steep.
Pythagorean Theorem:
a^2 + b^2 = c^2
2^2 + b^2 = 16^2
4 + b^2 = 256
b^2 = 252
b = 15.87 feet
To find out how high the ladder will reach, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the ladder is the hypotenuse, and the distance from the house foundation to the ladder is one of the other sides.
Using the Pythagorean theorem, we can set up the equation as follows:
(Height of the ladder)^2 = (Length of the ladder)^2 - (Distance from the house foundation)^2
Here, the length of the ladder is given as 16 feet, and the distance from the house foundation is given as 2 feet. Let's plug these values into the equation:
(Height of the ladder)^2 = (16 ft)^2 - (2 ft)^2
Simplifying,
(Height of the ladder)^2 = 256 ft^2 - 4 ft^2
(Height of the ladder)^2 = 252 ft^2
Now, to find the height of the ladder, we need to take the square root of both sides:
Height of the ladder = √(252 ft^2)
Calculating the square root,
Height of the ladder ≈ 15.874 ft
Therefore, the ladder will reach approximately 15.874 feet high up against the house.