A ladder resting against a wall forms an angle of 60 degree with the level ground. If the foot of the ladder is moved out from the wall 8ft. the ago forms with the ground is 45 degree. Find the length of the ladder.

1 answer

If the foot of the ladder started out at x ft away from the wall, then we know that the length of the ladder is 2x ft.

With a 45° angle, then the two legs are x+8 ft, and the length of the ladder is (x+8)√2.

So, now we have

2x = (x+8)√2
x(2-√2) = 8√2
x = 8√2/(2-√2)

the ladder is thus

16√2/(2-√2) = 16(1+√2) feet long