What is the value of θ for the acute angle in a right triangle?

Maybe I can put this picture to good use:

Now we can see that

θ + 58º = 90º

θ = 90º - 58º

θ = 32º

I don't really know what you mean by "for the acute angle in a right triangle," since both of the other angles in a right triangle are acute. But there are 2 angles that have the same sin as sin(32º) .

Those two angles are:

32º  (acute)      .....and.....      180º - 32º = 148º (obtuse)    

You make a a great maths detective Hectictar :)