Three camp sites, A, B and C, are planned for a hike and the distances
between the camp sites are 8km, 15 km and 9.5 km, as shown. If campsite
B is due north of camp site A, find the following, correct to 1 decimal place.
a. the bearing from campsite B to campsite C
b. the bearing from campsite C to campsite A
8 km
15 km
9.5 km

Step-by-step explanation:

For this, it can work well to find the measures of the triangle's interior angles at A and B. The law of cosines works well for this:

  cos(B) = (a² +c² -b²)/(2ac) = (8² +15² -9.5²)/(2·8·15) = 198.75/240 = 53/64

  B = arccos(53/64) ≈ 34.093°

Using the law of sines, we find ...

  sin(A) = a/b·sin(B) ≈ 0.472037

  A = arcsin(0.472037) ≈ 28.167°

a) The bearing from B to C is measured clockwise from North, so is the supplement of interior angle B.

  bearing to C = 180° - 34.1° = 145.9°

__

b) The bearing from C to A is 180° more than the interior angle at A, so is ...

  bearing to A = 180° + 28.2° = 208.2°

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step-by-step explanation:

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