Question

Island A is 210 miles from island B. A ship captain travels 230 miles from island A and then finds that he is off course and 180 miles from island B. What bearing should he turn to, so he is heading straight towards island B?

Answer 1

Let the point where the ship turns be C.

A, B and C form a triangle whose have length 230, 210 and 180 miles.


According to the cosine Law:

$|AB|^{2}= |AC|^{2}+|CB|^{2}-2|AC|*|CB|*cos(ACB)$

$210^{2}=230^{2}+180^{2}-2*230*180*cos(ACB)$

$44,100=52,900+32,400-82,800cos(ACB)$

$44,100=85,300-82,800cos(ACB)$

$82,800cos(ACB)=85,300-44,100$

$cos(ACB)= \frac{85,300-44,100}{82,800}=0.5$

Thus, m(ACB)=60°,

thus x=120°


Answer: x=120°