SOLUTION: 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.

Algebra ->  Trigonometry-basics -> SOLUTION: 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.       Log On


   

Question 1112316: 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. Hence find the bearing of C from B
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
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%2Fsin%28ACB%29 = 4.1%2Fsin%2853%29
Cross multiply
4.1 * sin(ACB) = 3.2*sin(53)
sin(ACB) = 2.55563%2F4.1
sin(ACB) =.6233
sin%5E%28-1%29%28ABC%29| = .6233
ACB ~ 39 degrees
:
find the bearing of C from B.
180 - 39 = 141 degrees