David wants to find the height of a building. He places his 646464 feet ladder against the very top of the building. David then measures the base of the building to his ladder which is 121212 feet. How tall is the building? Round your answer to the nearest tenth. Click Here for Help Video.

Question

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Answer 1

To find the height of the building, we can use the Pythagorean theorem, which relates the sides of a right triangle. In this case, the ladder forms the hypotenuse, 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.

Given:

• Length of the ladder (hypotenuse) = 6464 feet
• Distance from the base of the building to the ladder = 1212 feet
• Height of the building (let's call it \( h \))

According to the Pythagorean theorem: \[ a^2 + b^2 = c^2 \] where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the other two sides.

Here, we can set:

• \( a = h \) (height of the building)
• \( b = 1212 \) feet (distance from the ladder to the building)
• \( c = 6464 \) feet (length of the ladder)

Now we can write the equation: \[ h^2 + 1212^2 = 6464^2 \]

Calculating \( 1212^2 \): \[ 1212^2 = 1468944 \]

Calculating \( 6464^2 \): \[ 6464^2 = 41757696 \]

Now substituting these values into the equation: \[ h^2 + 1468944 = 41757696 \]

Next, we solve for \( h^2 \): \[ h^2 = 41757696 - 1468944 \] \[ h^2 = 40288752 \]

Now, we take the square root of both sides to find \( h \): \[ h = \sqrt{40288752} \approx 6357.5 \]

Rounding to the nearest tenth, the height of the building is approximately 6357.5 feet.

Answer 2

wrong

Answer 3

Let's go through the problem again step by step to solve for the height of the building correctly.

Given:

• Length of the ladder (hypotenuse) \( c = 64 \) feet
• Distance from the base of the building to the ladder \( b = 12 \) feet
• Height of the building \( h \) (what we need to find)

We will use the Pythagorean theorem: \[ a^2 + b^2 = c^2 \] In this case, we can set:

• \( h = a \) (height of the building)
• \( b = 12 \) feet (distance from the ladder to the building)
• \( c = 64 \) feet (length of the ladder)

Substituting the values we have: \[ h^2 + 12^2 = 64^2 \]

Calculating \( 12^2 \): \[ 12^2 = 144 \]

Calculating \( 64^2 \): \[ 64^2 = 4096 \]

Now we can write the equation: \[ h^2 + 144 = 4096 \]

Now, we solve for \( h^2 \): \[ h^2 = 4096 - 144 \] \[ h^2 = 3952 \]

Next, take the square root of both sides to find \( h \): \[ h = \sqrt{3952} \approx 62.8 \]

Rounding to the nearest tenth, the height of the building is approximately 62.8 feet. Thank you for your patience, and I apologize for the earlier errors!

Answer 4

David wants to find the height of a building. He places his 646464 feet ladder against the very top of the building. David then measures the base of the building to his ladder which is 121212 feet. How tall is the building? Round your answer to the nearest tenth.

Answer 5

Let's clarify the values given in your problem:

• Length of the ladder (hypotenuse) = 6464 feet
• Distance from the base of the building to the foot of the ladder = 1212 feet

We can use the Pythagorean theorem to find the height of the building. The Pythagorean theorem states that in a right triangle:

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

where \( c \) is the hypotenuse, \( a \) is one leg (height of the building), and \( b \) is the other leg (the distance from the base of the building to the foot of the ladder).

Given:

• \( c = 6464 \) feet (length of the ladder)
• \( b = 1212 \) feet (distance from the building to the ladder)
• \( h = a \) (height of the building, which we want to calculate)

Applying the Pythagorean theorem:

\[ h^2 + 1212^2 = 6464^2 \]

Calculating \( 1212^2 \): \[ 1212^2 = 1468944 \]

Calculating \( 6464^2 \): \[ 6464^2 = 41757696 \]

Substituting these values in: \[ h^2 + 1468944 = 41757696 \]

Now solve for \( h^2 \): \[ h^2 = 41757696 - 1468944 \] \[ h^2 = 40288752 \]

Now, take the square root of both sides to find \( h \): \[ h = \sqrt{40288752} \approx 6358.5 \]

Rounding to the nearest tenth, the height of the building is approximately 6358.5 feet.

Answer 6

Wrong Find the Height

Answer 7

I apologize for the confusion earlier. Let's solve for the height of the building correctly, clearly, and step-by-step this time.

Given:

• Length of the ladder: \(6464\) feet
• Distance from the base of the building to the foot of the ladder: \(1212\) feet

We need to find the height of the building, which we'll call \( h \).

We will use the Pythagorean theorem, which states: \[ a^2 + b^2 = c^2 \] where:

• \( a \) is the height of the building (what we're trying to find, \( h \)),
• \( b \) is the distance from the base of the building to the foot of the ladder (\(1212\) feet),
• \( c \) is the length of the ladder (\(6464\) feet).

1. Substitute into the Pythagorean theorem: \[ h^2 + 1212^2 = 6464^2 \]

2. Calculate \(1212^2\): \[ 1212^2 = 1468944 \]

3. Calculate \(6464^2\): \[ 6464^2 = 41757696 \]

4. Substitute those values into the equation: \[ h^2 + 1468944 = 41757696 \]

5. Solve for \(h^2\): \[ h^2 = 41757696 - 1468944 \] \[ h^2 = 40288752 \]

6. Now take the square root of both sides to find \(h\): \[ h = \sqrt{40288752} \approx 6342.0 \]

Rounding to the nearest tenth, the height of the building is approximately 6342.0 feet.

If I misunderstood the data or your premise is in error, please provide me with any corrections needed. Thank you for your patience!