Question 70757
{{{300=50/sin(d/2)}}} solve for d
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Replace d/2 by A for the time being to get:
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{{{300=50/sin(A)}}}
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Multiply both sides by sin(A) to get:
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{{{300*sin(A) = 50*sin(A)/sin(A)}}}
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Replace the sin(A)/sin(A) by 1. As a result the equation is:
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{{{300*sin(A) = 50}}}
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Divide both sides by 300 and get:
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{{{sin(A) = 50/300 = 1/6}}}
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Now by taking the arcsin(A) = 1/6 on a calculator you find that A = 9.5941 degrees.
But before we had decided that {{{A=d/2}}}. Therefore d = A*2. If we substitute 9.5941
degrees for A we get that d = 9.5941*2 = 19.0982 degrees.
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This is a principal solution.  It can be converted to radians by multiplying 19.0982
degrees by {{{pi/180}}}.
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Don't forget that sin(A) is also positive in the second quadrant.  Therefore, the angle 
170.4059 degrees is also a possible solution for A in sin(A) = 1/6. And since {{{A = d/2}}}
we can write 170.4059 degrees = d/2.  Solving for d we get 340.8118 degrees.
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Again these answers in degrees can be converted to radians by multiplying by {{{pi/180}}}.
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Hopefully this gives you a clue as to how to work this problem.