I think this has to do with using the pythagorean theorm, but I am not sure how I would solve it with only 1 value (24 ft). The length of the ladder would be the hypotenuse, which is why I think it is the pythagorean theorm.
Bottom of sign 24ft above ground. Ladder slid so bottom was half the distance to the base of the wall & top of ladder 9in above bottom of sign. how long ladder?
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What I can understand is that the base of the ladder is 12 feet from the base of the wall and that the vertical distance is 24+(9/12) = 24.75 feet above the ground.
So this is to obtain the Hypotenuse which using Pythagorean problem will be
L2= 122 +24.752 = 756.56 and the ladder length is 27.50 feet