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# cosine and sine rule

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why is it that when I solve for an angle, i get a decimal; and, when I put that decimal in to my calculator solving for the inverse of that angle, it gives me a number that i have to subtract from 180 to get my actual answer? Hopefully that makes sense. Here is the example

Find angle B   sinA=48.19 degrees

70/sinA = 90/ sinB

SinB= 90*sinA/70

90*sin48.19deg/ 70= 0.9582

inverse sin = 73.4 deg

the answer should be 106.6 deg

is this just the way it is or is there a better way of finding this answer? if this is the the only way it works, how do i know when to subtract my answer from 180?

Guest Apr 5, 2017
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There is no hard and fast rule, here....it depends upon the situation......however.....remember that sin (theta)  = sin (180 - theta).... and the inverse sine only returns angle values from -90° to 90°....so that's the reason that 106.6° will not be returned as an answer

If you know all three sides of a triangle.....the Law of Cosines will always produce the correct result

For example  if you know sides a, b and c ......you can find angle A  thusly

a^2  =  b^2 + c^2  - 2(b)(c)cos A

So

cos-1 [ ( a^2 - b^2  - c^2) / ( -2(a)(b)) ]   =   A

CPhill  Apr 5, 2017