(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I am having a nightmare doing homework for my physics test. I have figured out part of the answer but can not figure out what the angle of the displacement is and its driving me crazy...

The teacher showed us two methods of how to find the answers, but ended up making an error somehow on the first example which was never resolved, which is the one I am going by making it that much harder since I prefer that method(The other method is the one that you have to find Δd1x and Δd2x then Δd1y and Δd2y and go from there) It seems much simpler and he got the right answer using it vs the method mentioned earlier, but when I tried it the answer I got was even more far off so I clearly don't know where I am going with it. (maybe if someone is able to explain it to me, it would be more effective)

The question I can't figure out is "A dog runs after a ball 24m [W 12° S] and then heads 33m [E 52° S] after being distracted by a squirrel. What is his displacement?

2. Relevant equations

Δd1=24 [W12°S]

Δd2=33 [E52°S]

ΔdT=?

3. The attempt at a solution

I have drawn the triangle, and labelled its sides, decided the two distances create a 64° angle and so far have managed to find out the displacement is 31 meters by using the formula c^2=a^2+b^2-2abCOSc. My problem is figuring out the correct formula to obtain the angle. I've tried different methods and none of them work. The answer is supposed to be 31m[W84°S] this textbook has been wrong multiple times in the past however. Any help is appreciated as the test is tomorrow and I'm sure this will be on it.

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# Finding Displacement with angles and directions

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