A sinusoidal section is to be built as part of a roller coaster track. The high point is h=27 m at a horizontal distance d=0 m. It has a low point at h=-3 m at d=50 m.

a. Write an equation expressing h in terms of d.
b. The lengths of the horizontal timbers used to build the roller coaster's supporting structure are values of d. Calculate the length of the horizontal timber that is 4 m above the ground.

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