Orienteering is a sport that involves navigating your way to a series of checkpoints with the aid of a map and compass. The goal is to find each point on the map as quickly as possible. A typical compass used for orienteering is divided into 360 degree where 0 degrees is north and a bearing is measured clockwise from north.

Question

A.) Gabino and Mia are taking part in an orienteering course. They are instructed to walk 2.3 km on a bearing of 305 degrees to reach point A. There they are supposed to change their bearing to 64 degrees and walk 3.1 km to reach point B. Next they are supposed o return to their original position C. Explain why the interior angle formed at A must be 61 degrees. (The first part of the equation I had to draw the diagram but I don't know how to answer this part) Thanks in advance.

Answer 1

Draw a N-S line through A.

From that line, the angle back to the start is 55°, and the angle to B is 64°

55+64 = 119

That means the interior angle must be 61°, since the entire N-S line is a straight angle.

Answer 2

At point A, sketch in horizontals and verticals
the angle between AC and the x-axis is 35° , (305° - 270°)

So at A by alternate angles and parallel lines the angle between AC and the horizontal is 35°
And AB divides the right angle at A into angles of 64° , (the given angle) and 26°
So at A you have 35° + 26° = 61°

Of course if the rest of the question is to find BC, you would use the Cosine Law