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David wants to find the height of a building. He places his 54 feet ladder against the very top of the building. David then measures the base of the building to his ladder which is 7 feet. How tall is the building? Round your answer to the nearest tenth.

3 answers

To find the height of the building, we can use the Pythagorean theorem, which relates the lengths of the sides of a right triangle. In this case, the ladder forms the hypotenuse of the triangle, the height of the building is one leg, and the distance from the base of the building to the base of the ladder is the other leg.

Let:

  • \( h \) = height of the building
  • \( a \) = distance from the base of the building to the base of the ladder = 7 feet
  • \( c \) = length of the ladder = 54 feet

According to the Pythagorean theorem: \[ a^2 + h^2 = c^2 \]

We can substitute the known values into the equation: \[ 7^2 + h^2 = 54^2 \]

Calculating \( 7^2 \) and \( 54^2 \): \[ 49 + h^2 = 2916 \]

Now, subtract 49 from both sides: \[ h^2 = 2916 - 49 \] \[ h^2 = 2867 \]

Next, we take the square root of both sides to find \( h \): \[ h = \sqrt{2867} \approx 53.6 \]

Thus, the height of the building, rounded to the nearest tenth, is: \[ \boxed{53.6} \text{ feet} \]

wrong, broo

Let’s re-evaluate the problem step-by-step to ensure we arrive at the correct solution.

We have a ladder that is 54 feet long (this is the hypotenuse) and it rests against a building with the base of the ladder measuring 7 feet from the base of the building. We need to find the height of the building.

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

  • \( a \) = height of the building (which we want to find),
  • \( b \) = distance from the base of the building to the base of the ladder (7 feet),
  • \( c \) = length of the ladder (54 feet).

Substituting the known values into the equation: \[ h^2 + 7^2 = 54^2 \]

Now, calculating \( 7^2 \) and \( 54^2 \): \[ h^2 + 49 = 2916 \]

To isolate \( h^2 \), we subtract 49 from both sides: \[ h^2 = 2916 - 49 \] \[ h^2 = 2867 \]

Now, take the square root of both sides: \[ h = \sqrt{2867} \] Calculating \(\sqrt{2867} \approx 53.6\).

Upon double-checking, I confirm that my previous result is correct. The height of the building is indeed approximately: \[ \boxed{53.6} \text{ feet} \]

If there’s another aspect of the problem you think I’m missing, please let me know!