Law of sine and cosine problem
Just a simple problem. But I got stuck on some points.
We just learned the law of sine and the law of cosine from class.
And here's the assignment according this two topics:
Solve each triangle. Give lengths to three significant digits and angle measures to the nearest tenth of a degree.
a=8, b=5, ∠C=60°
Because we have the condition "SAS". So I used the law of cosine to solve for c.
Then all we need to do next is to find the two angles of the triangle, right?
So I used the sine law：
sin C/c=sin A/a
sin 60°/7=sin A/8
sin A= sin 60°*8/7
A= 81.8° and 98.2°
Here's where I got stuck. The answer at the very end of book only shows the answer 81.8°. But I think 98.2° is also acceptable. There should be two possiblities. Can somebody tell me why it doesn't fit?