# Angles & bearings confusion

• Aug 21st 2012, 05:08 AM
dontpanic
Angles & bearings confusion
Hi,

I've a similar problem to the one below but I don't quite understand how they arrived at the answer.

"A boat travels from point A, to B, to C, then back to A.

The bearing from A to B is S 27 degrees E
The bearing from B to C is N 57 degrees W
The bearing from C to A is N 16 degrees E

If this route was in the form of a triangle, what would the three angles of the triangle be?"

A = 16+27 = 43 degrees
B = 30 degrees
C = 107 degrees

I don't understand why 16+27 were added together to get A nor how B is 30. No matter what combination of subtracting or adding 90 degrees do I get 30.

Any help is much appreciated, Geometry & Trig are my weak points in Maths.
• Aug 21st 2012, 05:20 AM
Prove It
Re: Angles & bearings confusion
Quote:

Originally Posted by dontpanic
Hi,

I've a similar problem to the one below but I don't quite understand how they arrived at the answer.

"A boat travels from point A, to B, to C, then back to A.

The bearing from A to B is S 27 degrees E
The bearing from B to C is N 57 degrees W
The bearing from C to A is N 16 degrees E

If this route was in the form of a triangle, what would the three angles of the triangle be?"

A = 16+27 = 43 degrees
B = 30 degrees
C = 107 degrees

I don't understand why 16+27 were added together to get A nor how B is 30. No matter what combination of subtracting or adding 90 degrees do I get 30.

Any help is much appreciated, Geometry & Trig are my weak points in Maths.

The first step is ALWAYS to draw a diagram. From there you fill in whatever information you can from intuition, which is what I expect has happened here.
• Aug 21st 2012, 07:20 AM
dontpanic
Re: Angles & bearings confusion
After drawing a few diagrams I get it now,57-27=30: 16+27=43. 27 is got from 90-63 and 16 from 90-74. Had to make two right angle triangles and work it out from there. Still don't like trig though.
• Aug 21st 2012, 08:51 AM
emakarov
Re: Angles & bearings confusion
Attachment 24568

The blue angles are alternate interior and therefore equal, and similarly for the red angles. By assumptions, blue angles are 16 and red angles are 27. This gives A = 16 + 27 = 43 and B = 57 - 27 = 30.

Quote:

Originally Posted by dontpanic
Still don't like trig though.

But isn't it cool to solve a problem that can realistically apply to real life?