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.

Question

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.

oobleck · Answer

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