To find the height of the building, we can use the Pythagorean theorem. This theorem states that for a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this scenario, we can consider the ladder as the hypotenuse of a right triangle, with the height of the building as one side (opposite) and the distance from the base of the building to the ladder as the other side (adjacent).
Let:
- \( h \) = height of the building
- Length of the ladder = 808080 feet (hypotenuse)
- Distance from the base of the building to the ladder = 181818 feet (adjacent)
According to the Pythagorean theorem:
\[ \text{{(Length of ladder)}}^2 = \text{{(Height of building)}}^2 + \text{{(Distance from base)}}^2 \]
This can be written as:
\[ 808080^2 = h^2 + 181818^2 \]
Now we can solve for \( h \):
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Calculate \( 808080^2 \): \[ 808080^2 = 653036928640 \]
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Calculate \( 181818^2 \): \[ 181818^2 = 33000003224 \]
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Substitute these values into the equation: \[ 653036928640 = h^2 + 33000003224 \]
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Now, subtract \( 33000003224 \) from both sides: \[ h^2 = 653036928640 - 33000003224 \] \[ h^2 = 620036925416 \]
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Finally, take the square root to find \( h \): \[ h = \sqrt{620036925416} \approx 7899.7 \]
Rounding to the nearest tenth, the height of the building is approximately:
\[ h \approx 7899.7 \text{ feet} \]
So, the final answer is \( h = 7899.7 \) feet.