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Similar Triangles and Bearings

IGCSE,mathematics,past papers,revisions,triangles,geometry,bearings,trigonometry,similarity,angles,vertices,sides
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: 
IGCSE,mathematics,past papers,revisions,triangles,geometry,bearings,trigonometry,similarity,angles,vertices,sides
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.
IGCSE,mathematics,past papers,revisions,triangles,geometry,bearings,trigonometry,similarity,angles,vertices,sides
For the path taken by the junior students, let us start to find first the measure of the angles of the triangle formed.
IGCSE,mathematics,past papers,revisions,triangles,geometry,bearings,trigonometry,similarity,angles,vertices,sides
IGCSE,mathematics,past papers,revisions,triangles,geometry,bearings,trigonometry,similarity,angles,vertices,sides
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.
IGCSE,mathematics,past papers,revisions,triangles,geometry,bearings,trigonometry,similarity,angles,vertices,sides

Let us use triangle similarity to find the missing measurements.  
IGCSE,mathematics,past papers,revisions,triangles,geometry,bearings,trigonometry,similarity,angles,vertices,sides
IGCSE,mathematics,past papers,revisions,triangles,geometry,bearings,trigonometry,similarity,angles,vertices,sides
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