That's not a nice equation but here's what I might do: write it as 90 sin x= 144- 155.8 cos x
[itex]90\sqrt{1- cos^2 x}= 144- 155.8 cos x[/itex] and square both sides to get [itex]8100(1- cos^2 x)= 20736- 44870.4cos x+ 24273.64cos^2 x[/itex]. Solve that quadratic equation for cos x and then take the arccosine to find x. When you square both sides of an equation, that new equation may have roots that do not satisfy the original equation.
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