Question

A building is 2ft from a 10ft fence that surrounds the property. A worker wants to wash a window that is 14ft from the ground. He decided she should place the ladder 10ft from the nearest tenth of a foot, how long a ladder will he need

Answer 1

Height of fence = 10 feet

Height of point where window needs to be washed = 14 feet

Distance between fence and building = 2 feet

Distance between fence and ladder = 10 feet

⇒ Distance between building and ladder = Distance between fence and building + Distance between fence and ladder

⇒ Distance between building and ladder = 2 + 10 feet

⇒ Distance between building and ladder = 12 feet

Now to determine the length of the ladder that goes over the fence, we can use the Pythagoras theorem, where perpendicular is represented by the height of the building, and base is represented by distance between the building and the ladder, and the length of the ladder represents the hypotenuse

So by Pythagoras theorem:

H² = P² + B²

⇒ Length of the Ladder² = Height of the Building² + Distance between Ladder and Building²

⇒ Length of the Ladder² = 14² + 12²

⇒ Length of the Ladder² = 196 + 144

⇒ Length of the Ladder² = 340

⇒ Length of the Ladder = √340

⇒ Length of the Ladder = 18.439..

⇒ Length of the Ladder = 18.4

Hence, the length of the ladder should be 18.4 feet