Intro physics question involving magnitudes and vectors

Kevin Bertham
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You’re hanging from a chinning bar, with your ;arms at right angles to each other. The magnitudes of the forces exerted by both your arms are the same, and together they exert just enough upward force to support your weight, 620 N. (a) Sketch the two force vectors for your arms, along with their
resultant, and (b) use components to find the magnitude of each of the two “arm” force vectors.

So i drew the triangles out with 310 across the x-axis and 620 down.

The 90 degree angle as well as the two 45`s . I went to find the H which is cos 45= O/H , multiply by H on both sides so its H*cos45= 310 divide both by cos 45 which leaves you with H=310/cos45 which leaves with 438 N as the resultant. That is what i did anyway I don't think i am correct but if someone could give this a peak.
 
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lol they said i needed to follow the posting guidelines
 
Still true: use the template (you should also READ the guidelines ;-) )
 
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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