Shown in the figure is part of a design for a water slide. Find the total length of the slide to the nearest foot, if α = 25°, β = 31°, a = 35 ft, and b = 170 ft.

Let L be the total Length, so L=L1 + L2 + L3L1 is the first length

according to the figure L1 = a / sinβ = 25 / 0.57 = 43.85 ft L3 = a/sinα = 25 / 0.42=59.5 ft, for L2=b - L1-L3=96.62

so the total length is L=L1 + L2 + L3 = 200ft