A painter places an 8.5 ft ladder against a wall. The bottom of the ladder is 4 ft from the base of the wall. How high up the wall does the ladder reach?
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Pythagorean Theorem
a^2 + b^2 = c^2
a^2 + 4^2 = 8.5^2
Solve for a.
To determine how high up the wall the ladder reaches, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the ladder is the hypotenuse, and the distance from the base of the wall to the bottom of the ladder is one of the legs of the right triangle.
Let's call the height up the wall that the ladder reaches "h" ft.
According to the Pythagorean theorem, we have:
ladder^2 = height^2 + base^2
Substituting the given values, we have:
8.5^2 = h^2 + 4^2
Simplifying the equation:
72.25 = h^2 + 16
Now, let's isolate h^2 by subtracting 16 from both sides:
72.25 - 16 = h^2
56.25 = h^2
To find the value of h, we take the square root of both sides:
sqrt(56.25) = sqrt(h^2)
7.5 = h
Therefore, the ladder reaches a height of 7.5 ft up the wall.