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Using Pythagoras' theorem the length of the ladder is 20.248 feet
Regard the ladder as the hypotenuse and the distance from the wall as one leg of a right angled triangle. Then, 262 = 102 + H2 : where H is the height reached up the wall by the ladder. H2 = 676 - 100 = 576 : H = √576 = 24
12 feet.
Use Pythagoras' theorem: 122-32 = 135 and its square root gives the answer of 11.619 feet rounded to 3 decimal places