Question

Juana and Diego Gonzales, ages six and four respectively, own a strong and stubborn puppy named Corporal. It is so hard to take Corporal for a walk that they devise a scheme to use two leashes. If Juana pulls with a force of 23 lbs at an angle of 18° and Diego pulls with a force of 27 lbs at an angle of -15°, how hard is Corporal pulling if the puppy holds the children at a standstill?

Im trying to figure out how to set this up?

Answer 1

let AP be the vector of magnitude 23 lbs and direction 18°
and BP be the vector of magnitude 27 lbs and direction -15°

Complete the parallogram APBQ , with
AP=2
BP=27
angle P = 33°
then angle B = 180-33 = 147°
So PQ is the force pulling by the puppy to hold the kids

In triangle BPQ
BP=27
BQ=23
angle B=147
PQ^2 = 23^2 + 27^2 - 2(23)(27)cos147
PQ^2 = 2299.628...
PQ = √...
= 47.95 lbs