Problema Solution
A building is 2 ft from a 12 ft fence that surrounds the property. A worker wants to was a window in the building 17 ft from the ground. he plans to place a ladder over the fence so it rests against the building. He decides he should place the ladder 8 ft from the fence for stability. to the nearest tenth of a foot, how long of a ladder will he need?
Answer provided by our tutors
the ladder must clear the fence and then reach the building
let 'a' represent the angle the ladder makes with respect to the ground, then to clear the fence, then angle the ladder is placed at must satisfy this equation:
tan(a) >= 12/(8-2)
solving for 'a' gives a > 27
we also require that the length of the ladder be such that it can reach to the 17-foot mark of the building:
tan(a) >= 17/8
solving for 'a' gives a> 65
so an angle of 65 degrees will clear the fence and allow the ladder to reach the window
let 'x' represent the length of the ladder, then the length of the ladder is given by:
sin(65) = 17/x
solving for 'x' we have x=18.7574
the ladder needs to be 18.8 feet in length