Bearing and Trigonometry

A party of geographers is out on a field trip. They start walking from a church on a bearing of 223 degrees and walk in that direction for 3.5km to get to a lake. They then turn roughly east and walk on a bearing of 101 degrees. After walking for 6.6km it starts to rain heavily and they decide to abandon the trip and head straight back to the church for Shelter.

1. Create a scale drawing, state how far away from the group the church is when it starts to rain heavily and what three figure bearing the group needs to walk on in order to get back to it.
2. How long do you think it will take the group to walk back the church?

If you subtract 180 from 223 you get the back azimuth of 43° Take the next azimuth 101° and subtract 43° =58° that is the interior angle between the two lines with known azimuths and distances. From here you can use the cosine law and solve for the adjacent leg of the triangle. Then you can use the sin law to solve for the other interior angle and calculate the new azimuth.