Asked by Abdul
Three forces 20N, 30N, and 40N form a triangle. If the 40N force is the resultant R, then its angle θ, its direction, is computed using the Cosine Law. Compute the direction θ of R.
Answers
Answered by
oobleck
Draw the parallelogram using tip-to-tail vectors. Then
40^2 = 20^2 + 30^2 - 2*20*30 cosØ
so cosØ = 300/1200 = 1/4
Now, using the law of sines,
sinθ/20 = sinØ/40
sinθ = 1/2 * √15/4 = √15/8
40^2 = 20^2 + 30^2 - 2*20*30 cosØ
so cosØ = 300/1200 = 1/4
Now, using the law of sines,
sinθ/20 = sinØ/40
sinθ = 1/2 * √15/4 = √15/8