A building is 1 ft from a 10​-ft fence that surrounds the property. A worker wants to wash a window in the building 13 ft from the ground. He plans to place a l

Question

A building is 1 ft from a 10-ft fence that surrounds the property. A worker wants to wash a window in the building 13 ft from the ground. He plans to place a ladder over the fence so it rests against the building. (See the figure.) He decides he should place the ladder 9 ft from the fence for stability. To the nearest tenth of a foot, how long a ladder will he need?

Answer 1

So the base of the ladder will be 9 feet from the fence, which is 1 foot from the building, so it will be 10 feet from the building.  The top of the ladder will reach the window which is 13 feet above the ground.  So we have a right triangle with the ladder as the hypotenuse, and we know the two sides, so we can use the Pythagorean Theorem.

 

c² = a² + b²

c² = 13² + 10²

c² = 169 + 100

c = √269 = 16.40

 

So the ladder would need to be 16.4 feet long.