Expert: Sherry Wallin - 4/16/2011

Question
A student walks 50m on a bearing of N25E and then 200m due east. How far is she from her starting point? I have gotten my answer but i want to confirm my answer, because my textbook is telling me my answer is wrong

Answer
Ade~

The starting point is at the origin of an x-y coordinate system. Being told that the bearing is N25E just means that the pah the student will walk is one that is 25 deg to the right of north or of 90 deg. You are told that the student walks for 50 m and then abruptly turns east and walks another 200m.

                          
D    C ________________________B
|     /                  200m
|    /
|   / 50m
|  /
| /
A
You have a right triangle where the line segment AD goes vertical up the y-axis and so angle A (<DAC) measures 25 deg and the angle ACD is the complement of 90, thus 90-25 = 65 deg. Angle ACD plus angle ACB is a straight angle so we know that angle ACB is 180 - 65 = 115 deg. You now have enough info to use the law of cosines to find side c:

c^2 = a^2 + b^2 -2abCosC
c^2 = 200^2 + 50^2 -2(200)(50)Cos115
c^2 = 40000 + 2500 -20000Cos115
c^2 = 42500 -20000(-.423)
c^2 = 42500 +8460
c^2 = 50960


Is this what you got?

Math Prof
c = 225.74m