Dog Walker Precalc Question

Question

Two dogs are pulling on a dog walker. One pulls with a magnitude of 50N in the direction of 20° East of South. The other pulls at 75N in the direction of 10° North of East. Find the resultant magnitude and direction.

Im really having trouble with this question so any help would be great.When i work through it i end up with a .249 degree angle which i’m not sure is right.

Answer 1

If we use the standard map orientation and degree definition, then dog 1, 50 N 20° E of South, would be

(50 sin 20°, -50 cos 20°) dog 2 would be (75 cos 10°, 75 sin 10°)

Then, the total is (50 sin 20°+ 75 cos 10°, -50 cos 20° + 75 sin 10°) = (90.96, -33.96)

Then, the total force is √(90.96^2+(-33.96^2)) N in the directtion atan (33.96/90.96) South of East, or

97.09 N 20.47º South of East (or, if you prefer, 97.09 N 20º28' South of East)