You need the original shape, the scale of enlargement and the centre of enlargement.
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The scale or enlargement factor.
You need more information before you can calculate the base.
You take the information you're given, make sure you understand the question, write down the Pythagorean Theorem, then look at it to discover how it connects the information you have to the information you need to find.
You cannot with the information given. You need to know the densities of both components of the mixture.
It depends on what information about the rays is given. If all you have is two rays drawn on a sheet of paper then you need to measure the angle using a protractor. If their equations are given - in standard or vector form, then there are formulae that will enable you to work out the angle between them.