To reach a campsite, a hiker first walks for 2 mi at a bearing of N 40° E. Then he walks 3 mi due east. What are the magnitude and direction of his hike from his starting point to the campsite? Round the distance to the nearest tenth of a mile and the direction to the nearest degree.

4.55 mi N70°E, or 4.6 mi n70°E

Step-by-step explanation:

Draw a diagram; it helps keep the trig functions straight.

Starting from (0,0) a walk of 2 mi at N40°E leaves him at

x = 2sin40° = 1.29

y = 2cos40° = 1.53

Now, a walk 3 mi due east leaves him at

(4.29,1.53)

The new bearing is an angle θ with tanθ = 4.29/1.53 = 2.80

so, the new location is 4.55 mi N70°E