a 12 foot ladder is placed against a house to reach a window that is 9 feet high. how far away is the ladder from the house?

Question

This problem frustrated me because my teacher got 7.94 feet. Im offically confused. Help please

Answer 1

Use the Pythagorean Theorem, a²+b²=c².  The ladder is the hypotenuse (c = 12 feet) and the height of the window is one leg (a = 9 feet).  The last leg (b) is the distance of the ladder from the house.

 

a² + b² = c²

9² + b² = 12²

81 + b² = 144

 

Subtract 81 from both sides:

 

b² = 63

b = √63 = 7.94 feet

Answer 2

Let x = the distance from the base of the ladder to the house

 

By the Pythagorean Theorem, x² + 9² = 12²

 

                                                       x² = 144 - 81 = 63

 

                                                       x = √63 ≈ 7.94 ft