Which inverse trigonometric function will determine the measurement of angle B? tan -1(0.75)
cos -1(0.6)
cot (0.75)
sin -1(0.8)

1. WHAT DOES IT MEAN TO SOLVE A RIGHT TRIANGLE?  Every triangle has 3 angles and 3 sides.  A right triangle has one 90-degree angle and a hypotenuse, the side opposite the right triangle.

To "solve a right triangle," we must come up with the length of each of the 3 sides and the measures of the 2 angles beyond the 1 right triangle.

Example:  Given the right triangle with one of the smaller angles equal to 30 degrees and hypotenuse equal to 7, "solve" the triangle.  In other words, find the lengths of the 2 legs and the measure of the 3rd angle.  That angle is 90-30, or 60 degrees.  Thus, you have a 30-60-90 triangle.

One way to "solve" this triangle is to use the Law of Sines:

  a            b              c
= =
sin A      sin B       sin C.

If we let c = 7 and C = 90 deg, then the side length opposite the 30 degree angle is 

    a             7
=
sin 30     sin 90

and this simplifies to a(1) = (7)(sin 30) = 7/2

So now we know that one angle is 90 degrees, one is 30 and one is 60.

The 7 inch hypotenuse is opposite the 90 degree angle; the side opposite the 30 degree angle is 7/2, and the side opp. the 60 degree angle is 7sqrt(3)/2.