To determine how high the ladder will reach against the house, we can use the Pythagorean Theorem, which states:
\[ a^2 + b^2 = c^2 \]
where:
- \( a \) is the height the ladder reaches on the wall,
- \( b \) is the distance from the base of the ladder to the wall,
- \( c \) is the length of the ladder.
In this case, we have:
- \( c = 12 \) ft (the length of the ladder),
- \( b = 6 \) ft (the distance from the base of the ladder to the wall).
We need to find \( a \):
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Substitute the known values into the Pythagorean theorem: \[ a^2 + 6^2 = 12^2 \]
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Calculate \( 6^2 \) and \( 12^2 \): \[ a^2 + 36 = 144 \]
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To find \( a^2 \), subtract 36 from both sides: \[ a^2 = 144 - 36 \] \[ a^2 = 108 \]
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Now, take the square root of both sides to find \( a \): \[ a = \sqrt{108} \]
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To simplify \( \sqrt{108} \): \[ \sqrt{108} = \sqrt{36 \times 3} = \sqrt{36} \times \sqrt{3} = 6\sqrt{3} \]
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Now calculate \( 6\sqrt{3} \) approximately: \[ \sqrt{3} \approx 1.732 \] \[ 6\sqrt{3} \approx 6 \times 1.732 \approx 10.392 \]
Rounding to the nearest tenth, the height the ladder will reach is approximately:
\[ \text{Height} \approx 10.4 \text{ ft} \]
Therefore, the ladder will reach about 10.4 ft high on the house.
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