From the info given in the qns, you can tell that angle A is in quadrant 2, so you know what orientation your triangle has. And since sinA =3/5, you have the dimensions for 2 of the sides. Using pythagoras, you can find the third side. And this will be the triangle you will be using to solve the 3 parts.

The "trick" to such questions is that when the questions says "without using a calculator", you should be expecting yourself to do something like this.

Once you understand how to establish the triangle, the question becomes very straightforward.

For part ii, it's just a matter of recognizing that pi/2 is actually 90°, and that 90°-A means the other unknown angle.

For part iii, as long as you can recall your double angle formula, it's straightforward enough