I found this problem with the provided solution.
I already solved such type of problem, but using the triangle similarities and applying the Pythagorean theorem. This solution, however, is shorter. The only thing I can't get is how have got this (see in Bold below). Can someone elaborate a little bit more steps out there(on how we get from what equals tan A to the value of A in degrees)?
A fence 6 feet tall runs parallel to a tall building at a distance of 5 feet 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?
A = the angle the ladder makes with the ground
L = length of the ladder
L = 6/sinA + 5/cosA
dL/dA = -6cos/sin^2A + 5sinA/cos^2A = 0
-6cos^3A + 5sin^3A = 0
sinA/cosA = tanA = (6/5)^(1/3) = 1.06266
A = 46.73997 degrees
6/sinA = 8.23892
5/cos A = 7.29596
L = 8.23892 + 7.29596 = 15.53488 F