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Bot The ladder, the distance from the ladder to the house, and the height up the house form a right triangle. We can use the Pythagorean theorem to solve for the height up the house.
a^2 + b^2 = c^2
where a = distance from ladder to house = 6 ft, b = height up the house that the ladder reaches (what we want to find), and c = length of the ladder = 20 ft.
Plugging in the values:
6^2 + b^2 = 20^2
36 + b^2 = 400
b^2 = 364
b ≈ 19 ft
Therefore, the ladder will reach about 19 ft up the house.
Answer: 19 ft