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If you place a 24-foot ladder against the top of a 20-foot building, how many feet will the bottom of the ladder be from the bottom of the building? Round to the nearest tenth of a foot.

If you place a $24$ -foot ladder against the top of a $20$ -foot building, how many feet will the bottom of the ladder be from the bottom of the building? Round to the nearest tenth of a foot.

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Pythagorean theorem

Full solution

Q. If you place a

24

-foot ladder against the top of a

20

-foot building, how many feet will the bottom of the ladder be from the bottom of the building? Round to the nearest tenth of a foot.

Identify Triangle Sides: Identify the lengths of the sides of the right triangle formed by the ladder, the building, and the ground. $\newline$ The ladder forms the hypotenuse of the right triangle, the building forms one leg, and the distance from the bottom of the ladder to the building forms the other leg.
Find Unknown Length: We know: $\newline$ Ladder length (hypotenuse): $24$ feet $\newline$ Building height (one leg): $20$ feet $\newline$ We need to find the distance from the bottom of the ladder to the building (other leg), which we will call ' $x$ '.
Apply Pythagorean Theorem: Use the Pythagorean Theorem to find $x$ . The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse ( $c$ ) is equal to the sum of the squares of the lengths of the other two sides ( $a$ and $b$ ). $c^2 = a^2 + b^2$
Substitute Values: Plug in the known values into the Pythagorean Theorem. $\newline$ $24^2 = 20^2 + x^2$ $\newline$ $576 = 400 + x^2$
Solve for x: Solve for 'x'. $\newline$ $576 - 400 = x^2$ $\newline$ $176 = x^2$
Calculate Final Result: Take the square root of both sides to find $x$ . $\sqrt{176} = x$ $x \approx 13.3$ feet (rounded to the nearest tenth)

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