A boy walks 60m on a bearing of 035m and then 300m due east. How far is he from his starting point. With a diagram please.

Assuming you meant 35° and not 35 m

Of course you are on your own for the diagram, since we can't do
diagrams or images on this webpage, but on mine
I have triangle with sides 60 and 300 with an angle of 125° between, so
cosine law:
Let the third side be d
d^2 = 30^2 + 300^2 - 2(30)(300)cos125°
= 900 + 90000 + 10324.37
= ...
d = √...
= ?? (my answer is between 315 and 320 m)