Word problem involving the pythagorean theorem
a 12-ft ladder leans against the side of a house. the bottom of the ladder is 6-ft from the side of the house. how high is the top of the ladder from the ground ? if necessary, round your answer to the nearest tenth.
? ft

You can look at this as a triangle. The 12 ft ladder is the hypotenuse (c). The 6 ft distance at the bottom is a leg (a), and the unknown height is also a leg (b). So we don’t know the height, it’s variable will be x. The pythagorean theorem is a^2 + b^2 = c^2. the formula will be x^2 + 6^2 = 12^2. Solve as worked out in the picture, your answer is 10.4.