Attached is my working of the current problem, but i get an invalid solution. Any help would be appreciated
Sure, but you already did the hard part...
Starting with your equation (recall you took the derivative and set it equal to zero):
add to both sides:
multiplly both sides by and combine the trig functions:
Then take the cube root and inverse tangent to get x=0.7375. But you want the length of the ladder, so you have to plug in to the original equation:
Interesting, I was just doing this problem in a book I'm reading. The solution I found doesn't use the angle at all, but instead labels the lengths with new variable names and finds a relationship between them in terms of the known variables. The answer is given in terms of and and I thought you might find it interesting. It's attached to my reply.