A (vertical) fence 2.3 m high is located 1.2 m away from the (vertical) wall of a building. In this question, we shall take steps to find the shortest ladder that can reach the wall from the ground outside the fence.

(a) The two ends of the ladder are touching respectively the wall and the ground. We may also assume that the ladder touches the top of the fence, for otherwise the ladder could not be the shortest. If the ladder makes an angle of x radians with the ground, 0

Question

A (vertical) fence 2.3 m high is located 1.2 m away from the (vertical) wall of a building. In this question, we shall take steps to find the shortest ladder that can reach the wall from the ground outside the fence.

(a) The two ends of the ladder are touching respectively the wall and the ground. We may also assume that the ladder touches the top of the fence, for otherwise the ladder could not be the shortest. If the ladder makes an angle of  x radians with the ground, 0<x<2, then we can express the length, L (in meter), of the ladder in terms of x as follows:

anonymous · Answer

L = (A/sinx) + (B/cosx) where A and B are constants. Find them. 
(b) Find the limit of L as x approaches the endpoints 0 and pi/2 from the appropriate sides.
Answer: The limit of L as x approaches 0 from the right is _________, and the limit of L as x  approaches 2 from the left is ______________. 

(c) Find the value of x for which L attains its absolute minimum value. Hence, find the length of the shortest ladder. 

Answer: L attains its absolute minimum value when x = _______________ radians, and the length of the shortest ladder is _______ m