If you place a 29-foot ladder against the top of a building and the bottom of the ladder is 24 feet from the bottom of the building, how tall is the building? Round to the nearest tenth of a foot.


This is a right triangle problem where the ladder represents the hypotenuse, the distance from the bottom of the ladder to the building is one leg, and the height of the building is the other leg.

We can use the Pythagorean theorem to solve for the height of the building, which is the missing leg of the right triangle.

The Pythagorean theorem is:

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

Where:
- \(a\) is the height of the building (unknown),
- \(b = 24\) feet (distance from the bottom of the ladder to the building),
- \(c = 29\) feet (length of the ladder).

We solve for \(a\):

\[
a^2 + 24^2 = 29^2
\]

\[
a^2 + 576 = 841
\]

\[
a^2 = 841 - 576
\]

\[
a^2 = 265
\]

Now, take the square root of both sides:

\[
a = \sqrt{265} \approx 16.3
\]

So, the height of the building is approximately **16.3 feet**.

Would you like further details or have any other questions?

Here are 5 related questions for further practice:
1. What if the ladder was 40 feet long and placed 30 feet away from the building, how tall would the building be?
2. How would the angle between the ladder and the ground change if the ladder was 20 feet long and placed 15 feet away from the building?
3. If the height of the building is 20 feet, and the ladder is 25 feet, how far from the building is the bottom of the ladder?
4. How long must a ladder be to reach the top of a 50-foot building if it's placed 30 feet away from the building?
5. Can you determine the angle formed by the ladder and the ground in this problem?

**Tip:** The Pythagorean theorem only applies to right triangles, where one of the angles is exactly 90 degrees.

If you place a 29-foot ladder against the top of a building and the bottom of the ladder is 24 feet from the bottom of the building, how tall is the building? Round to the nearest tenth of a foot.

Learn how to calculate the height of a building using a 29-foot ladder placed 24 feet from the base of the building. This problem demonstrates the application of the Pythagorean Theorem to solve for the height, a key concept in geometry. Suitable for students in Grades 8-10.

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