- #1

This is the question:

An explorer is caught in a whiteout while returning to base camp. He was supposed to travel due north 5.6 km, but when the snow clears, he discovers that he is actually 7.8km at 50 degrees north of due east.

a)How far and b) in what direction must he now travel to reach base camp?

When I drew the sketch, it was a triangle. I think that I have the two values for two sides of the triangle: 5.6 km and 7.8 km. To determine how far, I think that I have to figure out the length of that other side.

90 degrees - 50 degrees = 40 degrees

I used 40deg as my angle to solve for the missing length of the triangle (a line connecting the location of where the explorer was lost to the location of the base camp).

So,

cos 40 = 5.6/d , where d is the distance

d = 7.31 km

Am I doing this correctly? Because I tried to do:

cos 50 = X/7.8 to see if I would get the distance from the origin to the base camp, but instead of getting 5.6 km I got 5.0 km, leading me to believe that my method was wrong.

Also, when they ask for direction, can I just say that the explorer has to move west? or should I include the degrees west he/she must travel?

Thanks.