Posted by Joe Schmo on Monday, January 3, 2011 at 8:18pm.
A fence 8 ft. tall runs parallel to a tall building at a distance 4 ft. from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building?

Calculus  drwls, Monday, January 3, 2011 at 10:22pm
Let L be the ladder length and A be the angle that the ladder makes with the ground. Convince yourself that
L = 4/cosA + 8/sinA
dL/dA = (4/cos^2A)*sinA (8/sin^2)*cosA
= 0 for minimum ladder length
sin/cos^2A = 2 cosA/sin^2A
sin^3A = 2 cos^3A
tanA = 2^1/3 = 1.260
A = 51.6 deg
Solve for L using the first formula above.

Calculus  Joe Schmo, Tuesday, January 4, 2011 at 7:38pm
Thank you very much! I just have one more question for you. How did you get L = 4/cosA + 8/sinA?

Calculus  marg, Wednesday, February 8, 2012 at 1:14am
a wall 10 feet high is 8ft from a house. what is the length of the shortest ladder that will reach the house when one end rests on the ground outside the wall?
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