If you place a 34-foot ladder against the top of a building and the bottom of the ladder is 25 feet from the bottom of the building, how tall is the building? Round to the nearest tenth of a foot.

Answer 1

To solve the problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this situation, the ladder serves as the hypotenuse, the height of the building is one side, and the distance from the building to the bottom of the ladder is the other side.

The formula can be written as: \[ a^2 + b^2 = c^2 \] where:

• \( c \) is the length of the ladder (hypotenuse),
• \( a \) is the height of the building,
• \( b \) is the distance from the wall to the bottom of the ladder.

Given:

• \( c = 34 \) feet (length of the ladder),
• \( b = 25 \) feet (distance from the ladder to the building).

We want to find the height \( a \) of the building.

1. Substitute the known values into the Pythagorean theorem: \[ a^2 + 25^2 = 34^2 \]

2. Calculate \( 25^2 \) and \( 34^2 \): \[ 25^2 = 625 \] \[ 34^2 = 1156 \]

3. Substitute these values into the equation: \[ a^2 + 625 = 1156 \]

4. Solve for \( a^2 \): \[ a^2 = 1156 - 625 \] \[ a^2 = 531 \]

5. Finally, we take the square root to find \( a \): \[ a = \sqrt{531} \approx 23.05167380558057 \]

Rounding to the nearest tenth: \[ a \approx 23.1 \]

Therefore, the height of the building is approximately 23.1 feet.

Answer 2

check your answer please

Answer 3

Let's recheck the calculations step by step using the Pythagorean theorem:

1. We have a right triangle where:
   • The length of the ladder (hypotenuse) is \( c = 34 \) feet.
   • The distance from the base of the ladder to the building is \( b = 25 \) feet.
   • We need to find the height of the building \( a \).

Using the Pythagorean theorem: \[ a^2 + b^2 = c^2 \]

Substituting the known values: \[ a^2 + 25^2 = 34^2 \]

Calculating \( 25^2 \) and \( 34^2 \): \[ 25^2 = 625 \] \[ 34^2 = 1156 \]

Now substituting these values back into the equation: \[ a^2 + 625 = 1156 \]

Now, isolate \( a^2 \): \[ a^2 = 1156 - 625 \] \[ a^2 = 531 \]

Next, take the square root of both sides: \[ a = \sqrt{531} \approx 23.05167380558057 \]

Rounding this value to the nearest tenth: \[ a \approx 23.1 \]

Thus, after rechecking the calculations, the height of the building is indeed approximately 23.1 feet. The calculations are consistent and correct. Thank you for prompting the recheck!