A 20 foot ladder is leaning aagainst a wall the base of the ladder is 7 feet away from the.wall hkw high up the wall will the ladder reacb
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To find out how high up the wall the ladder will reach, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the ladder) is equal to the sum of the squares of the other two sides (the height reached on the wall and the distance of the ladder from the wall).
In this case, we have a ladder of 20 feet leaning against a wall with the base of the ladder 7 feet away from the wall. Let's denote the height reached on the wall as "h".
Using the Pythagorean theorem, we can square the length of the hypotenuse (the ladder) and set it equal to the sum of the squares of the other two sides:
20^2 = 7^2 + h^2
Simplifying the equation:
400 = 49 + h^2
Subtracting 49 from both sides:
400 - 49 = h^2
351 = h^2
Taking the square root of both sides to solve for h:
√351 = √(h^2)
Approximately, h = 18.71 feet.
Therefore, the ladder will reach approximately 18.71 feet up the wall.
To find out how high up the wall the ladder will reach, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the ladder acts as the hypotenuse, the base of the ladder (7 feet away from the wall) acts as one side, and the height we want to find acts as the other side. The formula would be:
hypotenuse² = side₁² + side₂²
Let's plug in the values we have:
20² = 7² + side₂²
Simplifying the equation:
400 = 49 + side₂²
Subtracting 49 from both sides:
351 = side₂²
To solve for the height, we take the square root of both sides:
√351 ≈ 18.73
Therefore, the ladder will reach a height of approximately 18.73 feet up the wall.