Similar Triangles and Bearings

This item is taken from IGCSE Mathematics (0580) Paper 41 of May/June 2011.


To deal with this item, let us summarize the details of the problem:
   (a) Syllabus area: Trigonometry
   (b) Specific topic: Bearings, Similar Triangles
   (c) Concept Needed: 

Let us start with the path/route taken by the senior students. Let us determine first the length of all sides of their triangular path. Let us use the given that they walked a total of 18.9 km.

For the path taken by the junior students, let us start to find first the measure of the angles of the triangle formed.

From the given, it is stated that the junior students follow a similar path to that of the senior students. This suggests that the triangles formed by their paths are similar. Here are the corresponding measurements.

Let us use triangle similarity to find the missing measurements.  

---------------------------------------------------------------------------------------------------------------
Your comments and suggestions are welcome here. Write them in the comment box below.

Thank you and God bless!