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

#1**+2 **

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