Question

How to do this?

Answer 1

I tried it but I am not sure about it. I interpreted "possible" as the possibility to find the unknown quantity (angle).
Anyway, Alan gave a more interesting and complete reason in the comment below (I included Alan's comment in the answer).

Explanation:

The first and third can be solved in the sense that we can find a value of `theta` that satisfies the equation.

For example:

a. `sintheta=-2/5`

`theta=-23.578^@`

b. `tantheta=(85-22)/8`

`theta=82.763^@`

The second has two variables `alpha` and `beta` so that having only one equation we will not be able to solve it.

Alan N. tells us :
b is not possible. Irrespective of the values of `alpha` and `beta`, `sinalpha<=1` and `cosbeta<=1`.

Hence

`3sinalpha+4cosbeta<=7`