A spiral staircase turns 270 degrees as it rises 10 feet. The radius of the staircase is 5 feet. What is the number of feet in the length of the handrail? Express your answer as a decimal to the nearest tenth.
We call "un -wrap" the staircase to make a rectangle
The bottom of the rectange = (3/4) * 2pi * 5 = 7.5 pi ft
The height of the rectangle = 10 ft
The length of the handrail = the diagonal length of the rectangle =
sqrt [ 10^2 + ( 7.5 pi)^2 ] ≈ 25.6 ft
