GF is correct on the trig part, he used the Pythagorean Theorem to determine the length of the "hypotenuse", plus use of the unit circle for the trig angle, which assumes right angles are formed between the two legs. In this case the 90 and the 180 legs form a right angle, how convenient, so we can find arc tan (20/70) = ~16, so you would need to head 180 + 16 = 196 which he got. It is a simple trig relationship, it only works when the legs form right angles. Trig is based on the unit circle.
But I suspect you are trying to find a practical formula which is usable in the airplane without a calculator. Most pilots would simply do an intercept to the 180 and fly it outbound to the 70 DME fix. There are rules for deciding what intercepts to use based on DME values, let me get my sheet out for that. In this case I would use a 45 for this intercept, since it is so far away from the VOR. I can post those rules if I can find my sheet (yeah, I should know them!).