How Do You Calculate Theta for Vector Sum Using Component Method?

[AraProdieur]

Use the method of components to find the magnitude and direction of the vector sum R1, where R1 = A + B. The vector A = 15.2 m at an angle alpha = 180 degrees from the positive horizontal axis, and vector B = 17.2 m at an angle Beta = 41.3 degrees from the positive horizontal axis.
Answer= 11.5784

So far I have answered the first three parts, but am stuck on looking for the angle of theta 2; I don't understand this part.

Part 2= What is the angle theta 1 from the positive horizontal axis of the vector sum, R1? 101.348 degrees

Part 3= What What is the magnitude of the vector difference R2 where R2 = A-B? 30.4247

The following are the parts that I don't understand.

Part 4= What is the angle theta 2 of the resulting vector?

Part 5= What is thet magnitude of the vector difference R3 where R 3 = B - A? Answer= 30.4247

Part 6= What is the angle theta 3 of the resulting vector?

 

[G01]

Parts 4 and 6 are asking for the angles from the horizontal of the vectors found in the previous problems. Can you answer 5? If you were able to do 1 and 3, you should be able to do 5. If you can, you should also have the components of these vectors.

HINT: Can you use these components to find the angles?

 

[AraProdieur]

Parts 4 and 6 are asking for the angles from the horizontal of the vectors found in the previous problems. Can you answer 4 and 6? If you were able to do 1 and 3, you should be able to do 4 and 6. If you can, you should also have the components of these vectors.

HINT: Can you use these components to find the angles?

Yes, but in those parts, I used the law of sines and cosines, I didn't really use the components. But I do know the components although I don't know how to utilize them correctly. I'm also familiar with the usage of inverse tan, but other than that, I don't know how to do anything else with that.

 

[G01]

The problem statement was to use the component method, not the law of cosines, right?

If you used the component method, you'd have the components for the vector you would be trying to find. Using these x and y components, you should be able to find the angle the vector makes with the horizontal. Remember that a vector makes a right triangle with its components in which it is the hypotenuse. Can you use trig to find the angle using this triangle if you knew the components?