Answer:
- bearing of C from B: 145.9°
- bearing of A from C: 208.2°
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°
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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°
