You are probably more comfortable with triangles where the lengths are actual distances and not speeds- so think in terms of one second. If there were no current, in one second, at 4 ft per sec, the kayaker would have gone 4 ft across the river- his new postition would be "(4, 0)". If the kayaker were not paddling but just floating on the current, at 1 ft per sec, the kayaker would have gone 1 foot down river- his new position would be "(0, 1)". Key theoretical point: since velocity is a vector we can just add "components". With both paddling and current, the kayaker goes on the straight line from (0, 0) to (4, 1) which has a length of in one second. Yes, his speed would be feet per second (You did not include the units- that is an important part of the answer!).

A right triangle with "opposite side" of length 1 and "near side" 4 has angle degrees but that angle is measured to the triangle sideacross. You correct that the angle the kayak makes with the opposite side is 90- 14= 76 or degrees. But I don't see where you got that "North of East". There is nothing said in the problem, as you posted it, about the direction of the river.

Then the direction would just be

so the angle would be 75.96 degrees North of East

Thanks for any input