length of a ladder

Question

A ladder leans against a side of a building, making a 63-degree angle with the ground, and reaching over a fence that is 6 feet from the building. The ladder barely touches the top of the fence, which is 8 feet tall. Find the length of the ladder.

Answer 1

Sarah,

 

The ladder is placed outside the fence and it passes over the fence and then leans on the side of building.

 

Let the distance from foot of ladder to the fence be x feet

 

tan 63 = 8/x or x = 8 tan63 = 15.7 ft

 

Total distance from the foot of ladder to the building = 15.7 + 6 = 21.7 ft

 

Now cos63 = 21.7/length of ladder

 

Length of ladder = 21.7/cos63 = 47.8 feet