Halima Abdulahi Period 1

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Presentation transcript:

Halima Abdulahi Period 1 Pow & How #34 Halima Abdulahi Period 1

C is the angle opposite side c The rule of cosine Let a, b, and c be the lengths of the legs of a triangle opposite angles A, B, and C. The rule of Cosines is very useful for solving triangles It works for any triangle a, b and c are sides. C is the angle opposite side c

We know angle C = 37º, a = 8 and b = 11 The Law of Cosines says: c2 = a2 + b2 − 2ab cos(C) Put in the values we know: c2 = 82 + 112 − 2 × 8 × 11 × cos(37º) Do some calculations: c2 = 64 + 121 − 176 × 0.798… More calculations: c2 = 44.44... Take the square root: c = √44.44 = 6.67 to 2 decimal places Answer: c = 6.67 Example: How long is side "c" ... ?

The Rule of Sine The Law of Sines (or Sine Rule) is very useful for solving triangles a, b and c are sides. A, B and C are angles. (Side a faces angle A, side b faces angle B and side c faces angle C). It works for any triangle So when we divide side a by the sine of angle A it is equal to side b divided by the sine of angle B, and also equal to side c divided by the sine of angle C

Law of Sines: a/sin A = b/sin B = c/sin C Put in the values we know: a/sin A = 7/sin(35°) = c/sin(105°) Ignore a/sin A (not useful to us): 7/sin(35°) = c/sin(105°) Now we use our algebra skills to rearrange and solve: Swap sides: c/sin(105°) = 7/sin(35°) Multiply both sides by sin(105°): c = ( 7 / sin(35°) ) × sin(105°) Calculate: c = ( 7 / 0.574... ) × 0.966... Calculate: c = 11.8 (to 1 decimal place) Example: Calculate side "c"