Final answer:
Using the Pythagorean theorem, we calculated the height of the building by identifying the lengths of the ladder and its base from the wall, plugging those values into the theorem, and solving for the building's height. The building is approximately 36.74 feet tall.
Step-by-step explanation:
The question asks us to determine how high a building is if a ladder is leaning against it. We can solve this by using the Pythagorean theorem because the ladder, the wall of the building, and the ground form a right-angled triangle. The ladder represents the hypotenuse of the triangle, while the distance from the wall to the ladder's base represents one of the sides (lets call it 'a'), and the height of the building will be the other side (lets call it 'b').
According to the Pythagorean theorem:
a² + b² = c²
where 'a' is 12.8 feet, 'c' (the ladder's length) is 38.9 feet, and 'b' is the building's height which we need to find.
Here's the step-by-step calculation:
- Identify the lengths: a = 12.8 feet (distance from the building), c = 38.9 feet (ladder).
- Plug the known values into the theorem: 12.8² + b² = 38.9².
- Calculate a²: 12.8² = 163.84.
- Calculate c²: 38.9² = 1513.21.
- Subtract a² from c² to find b²: 1513.21 - 163.84 = 1349.37.
- Finally, take the square root of b² to find 'b': sqrt(1349.37) ≈ 36.74 feet.
Therefore, the height of the building is approximately 36.74 feet.