A painter leans a 20-ft ladder against a building. The base of the ladder is 12 ft from the building. To the nearest foot, how high on the building does the ladder reach?
This forms a right angle triangle.
a^2 + b^2 = c^2
a^2 + 12^2 = 20^2
a^2 + 144 = 400
a^2 = 256
a = 16
a=16
To find the height on the building that the ladder reaches, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, where a and b are the lengths of the two legs and c is the length of the hypotenuse, the following equation holds true: a^2 + b^2 = c^2.
In this case, the ladder is the hypotenuse, the base is one leg, and the height on the building is the other leg. Let's label the height on the building as "h".
So, we have:
12^2 + h^2 = 20^2
144 + h^2 = 400
To solve for h, we need to isolate the variable:
h^2 = 400 - 144
h^2 = 256
Taking the square root of both sides gives us:
h = √256
h = 16
Therefore, to the nearest foot, the ladder reaches a height of 16 feet on the building.
To find out how high on the building the ladder reaches, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the ladder acts as the hypotenuse, while the distance from the base of the ladder to the building forms one of the legs of the right triangle. Let's call the height the ladder reaches "h", and use "b" to represent the base of the ladder.
Using the Pythagorean theorem, we have:
h^2 = 20^2 - 12^2
Simplifying the equation:
h^2 = 400 - 144
h^2 = 256
Taking the square root of both sides:
h = √256
h = 16
Therefore, the ladder reaches a height of 16 ft on the building.