Calculate Tension in Cables Using Pythagorus Formula

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To calculate the tension in cables using the Pythagorean theorem, it is essential to first establish the angles and hypotenuse, which are already determined. With a hypotenuse of 23.3 m and angles of 31 and 59 degrees, the next step involves applying trigonometric functions to resolve the forces. Understanding that a system in mechanical equilibrium requires the vector sum of forces to equal zero is crucial for this calculation. Using sine and cosine functions will help derive the tension values from the known angles and hypotenuse. Proper application of these principles will yield the required tension in the cables.
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Well I've found the angles and got the hypotenuse by Pythagorus formula, but I'm kinda stuck i don't know what formula should i use to get the tension in cables.

Hyp=23.3 m
angles based on triangle AB we already have the 90 deg based on right angle triangle and the other angles are 31 and 59.

since I've got those what am i supposed to do after that.

appreciate all the help.
 

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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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