Use the definition of absolute value.

The absolute value is always non-negative. So if
is already non-negative,
is unchanged. But if
is negative, then
because multiplying
by -1 makes it positive.
Now, if
, then by the definition of absolute value,

Depending on what type of triangle it is, for a right triangle you would use sin inverse=(opposite/hypotenuse), cos inverse=(adjacent/hypotenuse), or tan inverse=(opposite/adjacent). For any other triangle you would refer to the Law of sines where side a/sine of angle A=side b/sine of angle B and same goes for C