A 44-foot ladder leans against a building. When the foot of the ladder is 10.8 feet from the base of the building, the ladder reaches the top of the building. How tall is the building? Round your answer to two decimal places

We can solve this problem using the Pythagorean Theorem, which is given as:

\[
a^2 + b^2 = c^2
\]

Where:
- \(a\) is the distance from the base of the building to the foot of the ladder (10.8 feet),
- \(b\) is the height of the building (which we want to find),
- \(c\) is the length of the ladder (44 feet).

Using the formula, we can solve for \(b\) (height of the building):

\[
b^2 = c^2 - a^2
\]
\[
b^2 = 44^2 - 10.8^2
\]
Now, let's calculate \(b\).The height of the building is approximately 42.65 feet.

Would you like more details on how this was calculated or have any other questions?

Here are some related questions for further exploration:
1. How would the height change if the ladder were longer?
2. What if the base of the ladder was closer to the building—how would that affect the height?
3. How would you calculate the angle the ladder makes with the ground?
4. What safety precautions are needed for leaning ladders at certain angles?
5. How does the Pythagorean theorem apply to other real-world structures?

**Tip:** Always check that the length of the ladder is longer than the distance from the wall to the ladder's base before solving.

A 44-foot ladder leans against a building. When the foot of the ladder is 10.8 feet from the base of the building, the ladder reaches the top of the building. How tall is the building? Round your answer to two decimal places.

Learn how to calculate the height of a building using the Pythagorean Theorem. In this problem, a 44-foot ladder leans against a building, with the foot of the ladder 10.8 feet from the base. Detailed step-by-step solution provided, including core geometry concepts. Suitable for students in Grades 9-12.

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