Find the resultant of these two force vectors using the following methods.

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The discussion focuses on finding the resultant of two force vectors, Fa (10.0N at 25.0 degrees) and Fb (5.0N at 45.0 degrees), using three methods: triangle, parallelogram, and mathematical. The user reports inconsistent results, with magnitudes of 14.80N, 15.39N, and 5.6N, and directions of 10 degrees, 30.31 degrees, and 37.6 degrees for each method respectively. The user has shared their drawings and calculations but is receiving feedback that the images are too small to assess. They are seeking advice on how to upload clearer images for better assistance. The thread highlights the challenges of vector addition and the importance of clear communication in problem-solving.
Brillntbrntt
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Homework Statement



Find the resultant of the following vectors using these methods: triangle method, parallelogram method and mathematical method.
Fa is a force vector with magnitude of 10.0N and makes an angle of 25.0 degrees with the x-axis. Fb is a force vector with a magnitude of 5.0N and makes an angle of 45.0 degrees with the x-axis. Specify both the magnitude and direction of the resultant vector.

I've tried doing this problem using the triangle, parallelogram, and mathematical methods and all of my results are coming out different each time.

The Attempt at a Solution


I've attached my drawings and processes by which I arrived to the solutions, but each time I'm getting a different number. The magnitudes I've gotten are 14.80N for the parallelogram, 15.39 N for the mathematical, and 5.6 for the triangle. Directions are P:10 degrees, M:30.31 degrees and T:37.6 degrees. Please help!

I apologize in advance if the image isn't clear.
 

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Sorry, your images are much too small to determine what calculations you have made.
 
I'm new to the forum and it will only allow me to upload one photo so I tried putting them altogether. Do you have any suggestions on how I can upload each one individually?
 
I tried it again. Please see if they are clear now.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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