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.