How far must he now travel to reach base camp?

[FriskeCrisp]

Homework Statement

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 4.4 km, but when the snow clears, he discovers that he actually traveled 7.8 km at 54° north of due east.
(a) How far must he now travel to reach base camp?
km

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

The Attempt at a Solution

First thing I did was draw a map of the problem using a coordinate plane. I have north be my y-axis and the x-axis as my due east. So I started at the x-axis and went 54 degrees up and then drew a line going out and labeled it as 7.8 km. Then I connected it to the point that was 4.4 km from the origin. When I did that, the lines formed a triangle. I then took the sin(36) = x/7.8 to get my x value. It came out to 4.584724968 km. Here is where I get lost. Is that now how far he has to travel to get to camp or is there something more that I am not getting?

 

[gerben]

The origin of your coordinate plane is where he started walking, 4.4 north of there is base camp. He ended up at 7.8 in direction 54deg from origin. The length of the straight line from where he ended up to base camp is how far he needs to travel.

 

[FriskeCrisp]

Ok I plugged that in and that was not the answer. Am I supposed to do something with vector addition?

 

[Sourabh N]

What answer did you get? Also give the values you plugged in.

 

[FriskeCrisp]

For the x value, I got 4.584724968. So my y-value is 4.4, my x value is 4.584724968, and the diagonal is 7.8

 

[Sourabh N]

You're supposed to reach 4.4 km on y-axis (the base). You're at 7.8 km at 54 deg. Write the two points in (x,y) component form. Now all you have to do is find distance between two points (x$$_{1}$$,y$$_{1}$$) and (x$$_{2}$$,y$$_{2}$$).

 

[gerben]

In you did your drawing correctly you have a triangle, the length of one side is 4.4 the length of another side is 7.8 and the length of the third side is the distance the explorer need to travel to bas camp.

You can figure this out by using some sines and or cosines of the given angles and the Pythagorean theorem

 

[FriskeCrisp]

finding the distance between two points did not work and neither did the Pythagorean theorem. The theorem gave a value of 6.440496875 however that was not the distance from where the traveler was to the base.