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Trigonometry

BEARINGS
  • The bearing of a point B from another point A is:
    • an angle measured from the north at A.
    • in a clockwise direction.
    • written as a three-figure number (i.e., 000° to 360°)
    • For example, the bearing of B from A is 050°
PYTHAGORAS THEOREM

  • To find the hypotenuse, c: c2 = a2 + b2
  • To find one of the shorter sides:
    • a2 = c2 – b2
    • b2 = c2 – a2
  • Angle of elevation: is the angles above the horizontal line.
  • Angle of depression: is the angle below the horizontal line.
  • Area of a triangle = ab/2 sin c
  • Ratios
    • Right angled Triangles:
      • sin x = opposite/hypotenuse [SOH]
      • cos x = adjacent/hypotenuse [CAH]
      • tan x = opposite/adjacent [TOA]
  • Sine Rule
    • a/sin a = b/sin b = c/sin c
    • One pair of information needed.
  • Cosine Rule
    • To find the angle when given 3 sides: cos a = (b2 + c2 – a2)/2bc
    • To find a side when given the angle and two sides: a2 = b2 + c2 – 2bc cos a
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