Hello, mlane!
If you have a right triangle and you only know 1 distance, how can you solve for the rest of the triangle>
We can't . . . we need one more piece of information.
If you take the inverse cosine of a ratio, does it give you an angle?
Yes, but we must be careful . . . it may not give us
the angle.
Suppose we are told that: \(\displaystyle \cos\theta\,=\,\frac{1}{2}\,=\,0.5\)
Our calculator says: \(\displaystyle \theta\:=\:\cos^{-1}(0.5)\:=\:60^o\)
. . and it checks out:
.\(\displaystyle \cos(60^o)\:=\:0.5\)
But it is also true that: \(\displaystyle \cos(300^o)\,=\,0.5\)
. . and \(\displaystyle \cos(-60^o)\,=\,0.5\) . . . and \(\displaystyle \cos(420^o)\,=\,0.5\)
Which of these is the correct answer?
.It depends on the nature of the problem.
