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Math Help - Law of sines word problem

  1. #1
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    Post Law of sines word problem

    A ferris wheel has 16 evenly spaced cars. The distance between adjacent chairs is 15.5 ft. Find the radius of the wheel (to the nearest 0.1 ft).

    I have no idea where to start..any help is appreciated!
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  2. #2
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    Quote Originally Posted by live_laugh_luv27 View Post
    A ferris wheel has 16 evenly spaced cars. The distance between adjacent chairs is 15.5 ft. Find the radius of the wheel (to the nearest 0.1 ft).

    I have no idea where to start..any help is appreciated!
    If the cars are evenly spaced, then the angle between each radius is \frac{360^{\circ}}{16} = 22.5^{\circ}.

    The distance between adjacent chairs is 15.5\textrm{ft}.

    Let r be the radius of the ferris wheel.

    You now have an isosceles triangle with the equal lengths r\textrm{ft} and the angle between them is 22.5^\circ.


    Can you find the other two angles? Can you formulate a Sine Rule equation?
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    If you don't know the sine law, draw a perpendicular from the vertex of the isosceles triangle to the base so that you have two right triangles with "opposite side" of length 15.5/2= 7.75 feet, angle 22.5/2= 11.25 degrees, and hypotenuse of length r.

    (I thought of doing this as a circle of circumference 15.5*16 but that is a digit off in the first decimal place.)
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