<PRE><B>Question 1112316</B>
Karl rode his horse 3.2 km from A to B on a bearing of 037°.
 He then turned and rode 4.1km to C, which is due east of A.
 Find the size of angle ACB, correct to the nearest degree.
:
The bearing of A to B is referenced to a north/south line, therefore C, being east, would form a 90 degree with the north/south line, therefore
:
Angle BAC: 90 - 37 = 53 degrees
Use the law of sines to find ACB
{{{3.2/sin(ACB)}}} = {{{4.1/sin(53)}}}
Cross multiply
4.1 * sin(ACB) = 3.2*sin(53)
sin(ACB) = {{{2.55563/4.1}}}
sin(ACB) =.6233
{{{sin^(-1)(ABC)}}}| = .6233
ACB ~ 39 degrees
:
find the bearing of C from B.
180 - 39 = 141 degrees
</PRE>