An explorer is caught in a whiteout (in which the snowfall is so thick that the ground cannot be distinguished

Question

An explorer is caught in a whiteout (in which the snowfall is so thick that the ground cannot be distinguished from the sky) while returning to base camp. He was supposed to travel due north for 5.3 km, but when the snow clears, he discovers that he actually traveled 7.8 km at 46° north of due east.

(a) How far must he now travel to reach base camp?

(b) In what direction must he travel?(counterclockwise from due east)

Answer 1

Lets take the distance he actually walked and break it up into components:
North:
7.8sin46 = 5.61085km
So he walked 5.61085 - 5.3 = 0.31085km too far north.
East:
7.8cos46 = 5.41834km
He has to walk:
Distance = √[(5.41834)^2 + (0.31085)^2] = 5.42725km
Direction = 180 + arctan(0.31085/5.41834) = 183.283 degrees ccw from due east.