To find out how high the top of the ladder is touching the house, we can use the Pythagorean theorem. The ladder, the distance from the base of the house to the bottom of the ladder, and the height at which the ladder touches the house form a right triangle.
Let:
- \( c \) be the length of the ladder (the hypotenuse), which is 20 feet,
- \( a \) be the distance from the base of the house to the bottom of the ladder (one leg of the triangle), which is 5 feet,
- \( b \) be the height at which the ladder touches the house (the other leg of the triangle).
According to the Pythagorean theorem: \[ c^2 = a^2 + b^2 \]
Plugging in the values: \[ 20^2 = 5^2 + b^2 \] \[ 400 = 25 + b^2 \] Now, subtract 25 from both sides: \[ 400 - 25 = b^2 \] \[ 375 = b^2 \]
To find \( b \), take the square root of both sides: \[ b = \sqrt{375} \]
Calculating \( \sqrt{375} \): \[ b \approx 19.364 \]
Rounding to the nearest tenth: \[ b \approx 19.4 \]
Therefore, the height above the ground at which the top of the ladder is touching the house is approximately 19.4 feet.
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