Solving Angle & Triangle Problems: 2Tsin(angle) = 3mg

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THis isn't exactly a question however, its a method my teacher talked to me about and I don't quite understand.

This is a way of getting greater accuracy, and attaining the higher grades.

The question states, tan(angle) = 3/4
So instead of using tan^-1 (3/4) to get the angle with many digits, round it off and losing accuracy, she said:

Drawing the triangle out results in:
http://imgplace.com/directory/dir51/1172694216_triangle.JPG
Using pythag you can work out the other side.

Now you have:
sin(angle) = 3/5
cos(angle) = 4/5

I have worked out the statement:
2Tsin(angle) = 3mg

However, how do I apply what was attained from the triangle to this question?
Thanks.
 
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