Question

A 32 foot ladder lean against a building so that the top of the ladder touches the building at a point 23ft above the ground. To the nearest tenth of a foot, how far from the bottom of the building is the bottom of the ladder? A 22.2 ft B. 39.4 ft C. 27.5 ft D. 30.1 ft

Answer 1

We must assume the wall of the building is vertical.  The hypotenuse of this right triangle is represented by the ladder, 32 feet.  So we wish to find the bottom of the triangle, the distance between the wall and ground.  From the infamous Pythagorean theorem, the sum of the squares of the sides equals the square of the hypotenuse.

Taking the difference, 32² - 23² = 1024 - 529 = 495.  What is the square root of 495?  It is 22.2 feet.  I would move the ladder closer or get a shorter ladder--that does not seem stable.