How far from the base of the house do you need to place a 13-foot ladder so that it exactly reaches the top of a 10- foot tall wall?
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To solve this problem, 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.
Let's denote the distance from the base of the house to the placement of the ladder as x.
Using the theorem, we have:
x^2 + 10^2 = 13^2
Simplifying the equation:
x^2 + 100 = 169
Subtracting 100 from both sides:
x^2 = 69
Taking the square root of both sides to solve for x:
x = √69
Approximating the square root of 69, we have:
x ≈ 8.31
Therefore, you need to place the ladder approximately 8.31 feet from the base of the house so that it exactly reaches the top of the 10-foot tall wall.
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