You are running into what is called the "ambiguous case" . For example
sin 30° = sin 150° = .5
because the sine is positive in the II and III quadrant.
So If you start with sinØ = .5
your calculator is programmed to always give the closest angle to 0, and that would be 30°
You probably used the cosine law to find the first angle. A suggestion is to always find the largest angle first. If that happens to be an obtuse angle, your calculator will find the correct angle.
Of course there can only be one obtuse angle in a triangle, so using the sine law for your second angle does not result in any problems
notice that in your solution 78 and 102 add up to 180 , and sin 78 = sin(180-78) = sin 102
I would have found angle S first, the largest angle always opposite the largest side.
7^2 = 5^2 + 4^2 - 2(5)(4)cosØ
40cosØ = -8
cosØ = -8/40 = -1/5
Ø = 101.537°
Now you can use the sine law and you will find the correct other angles.
In triangle RST, RS=4, RT=7, and ST=5. Determine the measures of the angles to the nearest degree.
I solved correctly for T's angle of 34 degrees. Once I try using the sine law to solve for angle S, I keep getting 78 degrees, when it's supposed to be 102 degrees. I tried solving for R first, and it worked that way using sine law, but why won't solving for angle S first work out?
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