Pre-Calc

Please help me with this word problem, I can't seem to figure it out.

Both Derek and Sam are 5ft 10in tall. Derek looks at a 10ft basketball goal with an angle of elevation of 29 degrees, and Sam looks at the goal with an angle of elevation of 43 degrees. If Sam is directly in front of derek, how far apart are the boys standing?

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  1. Draw a side view of the situation, then the basket is 50 inches above the height of the the eyes of the two boys.
    distance of derek to point below the basketball is x
    of Sam to a point below the basketball is y

    tan29 = 50/x ---> x = 50/tan29
    tan 43 = 50/y --->y = 50/tan43

    distance between the boys = x-y
    = 50/tan29- 50/tan43
    = 36.583 inches
    = or 3.05 ft

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