I know what question your talking about.
arctan is the same as tan^-1 (look on your calculator)
it finds the angle (theta) when your given the lengths of the triangle.
so if asks, as an example, the arctan of .5, it would be 26.5 degrees.
Youre really not gonna have to find the actual angle on the MCAT
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This is probably what you are looking for:
So if you want to find the length of the sides of the triangle, and you don't know theta, or the lengths of any side of the triangle, if they give us theta= arctan of .5
We know that tan is opposite/adjacent, so .5 would mean 1/2, or the side opposite to theta has a length of 1, and the side adjacent has a length 2, so then we can find the hypotenuse, and solve the problem.
So its really just werid the way they word it. They chould have said the Tan (theta) = .5 , which is the same thing as theta = arctan .5
Try in it your calculator. Tan(26.5) = .5 , arctan(.5) = 26.5
Hope this helps