Question
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?
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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.
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.