The route followed by a hiker consists of three displacement vectors A, B , and

Question

The route followed by a hiker consists of three displacement vectors A, B , and C . Vector A is along a measured trail and is 1710 m in a direction 23.0 ° north of east. Vector B is not along a measured trail, but the hiker uses a compass and knows that the direction is 39.0 ° east of south.
Similarly, the direction of vector C is 43.0 ° north of west. The hiker ends up back where she started, so the resultant displacement is zero, or A + B + C = 0.
Find the magnitudes of (a) vector B and (b) vector C.

I know this question is supposed to be easy, but I think I'm missing something when I go to find the length of each of these vectors. Do these vectors even make a triangle? Please help me find the magnitudes of these vectors.

Explanation / Answer

I think the easiest method (and hence the one less likely to make mistakes) is to calculate all the internal angles of the triangle using basic geometry, then use the Law of Sines. The angles are (where a=angle opposite vector A etc) b = 23+43 = 66 deg c = 39+(90-27) = 102 deg a = 180-b-c = 12 deg Magnitude of vector B = 1710*sin(66)/sin(12) = 7513.58m Magnitude of vector C = 1710*sin(102)/sin(12) = 8044.92m please dont forget to rate my answer :)

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.