Question

two dogs pull horizontally on ropes attached to a post; the angle between the rope is 70deg. dog A exerts a force of 268N and dog B exerts a force of 310N.
find the magnitude of the resultant force. and the angle the resultant force makes with dog A`s rope.

Answer 1

draw the figure.
In my head, if R is the resultant

Then the law of cosines

R^2=268^2+310^2-2*268*310Cos70

The angle can be found by the law of sines, but you need to draw the figure and see how that works, after you get the angle in the law of sines, you have to orient it with geometry to some axis.

Answer 2

58651.481

Answer 3

Fr=268[0o] + 310[70o] = 268 + 310*Cos70 + (310*sin70)i = 268 + 106 + 291i = 374
+ 291i = 474N[37.9o] N. of E. = 37.9o N.
of dog A's rope.