SOLUTION: I need to find the solution for d. 300=50/sin(d/2)

Question 70757: I need to find the solution for d. 300=50/sin(d/2)
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
solve for d
.
Replace d/2 by A for the time being to get:
.

.
Multiply both sides by sin(A) to get:
.

.
Replace the sin(A)/sin(A) by 1. As a result the equation is:
.

.
Divide both sides by 300 and get:
.

.
Now by taking the arcsin(A) = 1/6 on a calculator you find that A = 9.5941 degrees.
But before we had decided that . Therefore d = A*2. If we substitute 9.5941
degrees for A we get that d = 9.5941*2 = 19.0982 degrees.
.
This is a principal solution. It can be converted to radians by multiplying 19.0982
degrees by .
.
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
we can write 170.4059 degrees = d/2. Solving for d we get 340.8118 degrees.
.
Again these answers in degrees can be converted to radians by multiplying by .
.
Hopefully this gives you a clue as to how to work this problem.
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