A 15.5 foot ladder leaning up against the building .the base is 8.2 feet away from the building .how far up does the ladder reach against the building.
√(15.5² - 8.2²) = 13.2 ft
To find out how far up the ladder reaches against the building, we can use the Pythagorean theorem. The Pythagorean 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 forms the hypotenuse of a right triangle, with the base of 8.2 feet being one side, and the distance up the building being the other side. Let's call the distance up the building 'x'.
Applying the Pythagorean theorem:
Hypotenuse^2 = Base^2 + Height^2
15.5^2 = 8.2^2 + x^2
Simplifying:
240.25 = 67.24 + x^2
Subtracting 67.24 from both sides:
x^2 = 172.01
To find the value of 'x', we can take the square root of both sides:
x = √172.01
Using a calculator, we find that the square root of 172.01 is approximately 13.11.
So, the ladder reaches approximately 13.11 feet up against the building.