A 17 feet ladder is placed against a building. The bottom of the ladder is 15 feet away from the building. How many feet high is the top of the ladder?
Using the Pythagorean theorem, we can solve for the height of the ladder. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (ladder) is equal to the sum of the squares of the other two sides.
Let's denote:
Height of the ladder (top of the ladder) = h
Distance of the bottom of the ladder from the building = b
Length of the ladder (hypotenuse) = c
Given:
Length of the ladder = 17 feet
Distance of the bottom of the ladder from the building = 15 feet
Applying the Pythagorean theorem:
c² = h² + b²
Plugging in the given values:
17² = h² + 15²
289 = h² + 225
h² = 289 - 225
h² = 64
Taking the square root of both sides:
√(h²) = √64
h = 8 or h = -8
Since height cannot be negative, the height of the top of the ladder is 8 feet.
This problem forms a right triangle, where the ladder is the hypotenuse, the distance from the bottom of the ladder to the building is one side, and the height of the building is the other side. To find the height of the building, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
Let's label the height of the building as 'h' and the distance from the bottom of the ladder to the building as 'd'.
According to the problem, the distance 'd' is 15 feet and the length of the ladder is 17 feet.
Using the Pythagorean theorem, we have:
h^2 + d^2 = ladder length^2
Plugging in the given values:
h^2 + 15^2 = 17^2
h^2 + 225 = 289
Subtracting 225 from both sides:
h^2 = 289 - 225
h^2 = 64
Taking the square root of both sides:
h = √64
h = 8 feet
Therefore, the top of the ladder is 8 feet high.