There is a right triangle with a left side of six, a bottom side of 10, and a hypoteneuse 11.66. How do you find the other two angles? I tried the inverse of tangent 6/11.66, but my calculator said that's invalid. What do you properly do?

Answer 1

You probably omitted some parentheses or pressed the wrong keys.
The inverse tangent of 6/11.66 exists, but does not represent the angle you are looking for.
Lets go back to the definition of the tangent, which is
tangent(θ)=opposite/adjacent.
If we consider the right-angle to be on the left, and the angle θ on the right of the bottom side of 10, then
opposite = 6,
adjacent = 10
θ = arctangent(6/10) = approx. 31°
The top angle can be obtained by subtraction,90°-θ

Answer 2

also tangent is opposite over adjacent