A 24-foot ladder is placed against a building. The building is perpendicular to the level ground so that the base of the ladder is 11 feet away from the base of the building. How far up the building, in feet, does the ladder reach? Round to nearest hundredth.
To find how far up the building the ladder reaches, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the ladder forms the hypotenuse of a right triangle, and the distance up the building is one of the other two sides.
Let's call the distance up the building "x" feet.
So, according to the Pythagorean theorem:
(11^2) + (x^2) = (24^2)
Simplifying this equation, we have:
121 + (x^2) = 576
Subtracting 121 from both sides, we get:
x^2 = 455
To solve for x, we take the square root of both sides:
x = √455
Using a calculator, we find that √455 is approximately equal to 21.33.
Therefore, the ladder reaches approximately 21.33 feet up the building.
x^2+11^2 = 24^2
now just solve for x