Explanations & Calculations
- Refer to the sketch attached.
- Two forces can be rearranged in a vector triangle as shown where laws of sines & cosines can be applied then.
- Due to the geometry the angle BOA = 40 degrees
- And the angle OBA can be found to be (190−θ)
- Then by cosine rule, the magnitude of the resultant can be found
cos400.7660R=2OB×OAOB2+OA2−AB2=2×8×1082+102−R2=6.437N
- If it makes an angle θ with the north, then using sine rule,
sin(190−θ)10sin(190−θ)190−θθ=sin40R=0.99858=86.946=103.050[NofE]
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