CraigsMaths

If you travel 50° for 5 kms and then 165° for 2 kms are far are you from your starting point?  These types of problems are used all the time.  See triangulation.  They are easily solved using the sin, cos and tan trigonometry ratios and a few basic rules of geometry.

General process

All these problems can be solved by following these general steps.  Not all problems will use all steps but if you are having difficulty think through each step and see what would happen if you did use it.

Step 1: Convert speeds into distances travelled and compass direction bearings into three digit bearings.

Step 2: Draw a clear diagram.

In your diagram:

• Label all points with a suitable letter.
• Make sure all units are the same for distance and direction.
• Draw the compass at the starting points or ‘from’ points.  These are the points from which you will want to determine direction and distance.
• Draw in the known angles from the bearings given.

Step 3: Identify and complete the triangles in your diagram that need to be solved.

Step 4: Determine as many of the internal angles of triangles formed as you can using :

• Difference of two known angles where the smaller angle is included in the larger.
• Straight angle is 180°.
• 360° in a full circle.
• Sum of angles in a triangle is 180°.
• Co-interior angles sum to 180°.
• Alternate angles are equal.

Step 5: Label unknown distances and angles with pronumerals.

Step 6: Using your diagram identify the angles and distances that are being asked for by the question.

Step 7: Decide if you need to use:

• For right angle triangles:
  • Sine
  • Cosine
  • Tangent
  • Pythagoras
• For other triangles:
  • Cosine rule
  • Sine rule

Step 8: Calculate the required angles and distances.

Step 9: Make sure your answers are given in the required units and accuracy.

Tuesday, October 13th, 2009 at 1:19 pm
Category: Trigonometry.
Comments RSS 2.0 feed.