A rope hangs from the ceiling. It reaches the floor exactly. It's 4 feet from the wall. When it's pulled to the wall, the end of the rope is 4 inches above the floor. How high is the ceiling?

Answer 1

L(1-cosT) = 1/3 foot
sin T = 4 feet/L so L sin T =4

1-cosT = 1/3L
L sinT = 4

cosT = (3L-1)/3L
so cos^2T = (9L^2 -6L+1)/9L^2
so 1-cos^2T = (6L-1)/9L^2
which is sin^2 T
but
sin^2T =16/L^2
so
16/L^2 = (6L-1)/9L^2
144 = 6L-1
6L = 145
L = 24.2 feet
check my arithmetic!

Answer 2

4" is 1/3 foot. So,

(h - 1/3)^2 + 4^2 = h^2

Damon is correct. 24'2"