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

Answer 1

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

Answer 2

thank you soo much :)

Answer 3

can you show us the diagram and tell the reason why we have to use sin and cos

Answer 4

can you tell us in the diagram which is x and which is y please