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)?

Thanks,

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?

Let:

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