From A,B lies 11 km away on a bearing of 041 degrees and c lies 8 km away on a bearing of 341 degrees.Find the distance between b and c and bearing of b from c.

Question

Answer are given 9.8 km and 085.7 degrees

Answer 1

if you lay the points on a circle with origin at A, you will get a triangle with an interior angle of 60 deg at A, which is the sum of the bearing of 41 deg between A and B, and 360deg-341deg= 19 deg, the beraing between points A and C. let a be the side opposite to angle A at point A, you know the distances between A and B call that side

c =11km opposite to angle C, and side b =8km opposite to angle B.

 

Using the law of cosines:

 

a² = b² + c² - 2 bc cos A

a² = 8² + 11² - 2 (8)(11) cos 60

a² = 97, a = 9.8 km

 

Now you need the bearing of B from C 

From the law of Sines find the angle C at point C 

 

9.8/sin60 = 11km/sin C, sin C = (sin60x11km)/(9.8km)=0.972

 

sin^-1sin C = 75.3 degrees

 

The bearing of B from C is the angle formed by the line joining C and B and rotating about C. By Geometry this angle is

180 - sum( Angle C + 19 deg ) = 180-(75.3+19)=85.7 deg

 

You need to draw this as I described so you can understand it. I don't have the capability to draw graphs in this window. That is why we have the online classroom so this can be better explained..