word problem of a ladder

Question

if a 16-foot ladder is 6 feet from a wall, how many feet up the wall will it reach?

Answer 1

Let x = distance from the base of the wall to the top of the ladder.

 

The ladder, wall, and ground form a right triangle with legs of lengths

x feet and 6 feet and hypotenuse of length 16 feet.  

 

By the Pythagorean Theorem, x² + 6² = 16².

                                          x² + 36 = 256

                                                 x²  = 220

                                                 x ≈14.8 feet