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?"

**Answer**

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.

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?"

**Answer**

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.

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.

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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?