The boat is to be pulled onto the shore using two ropes. If the resultant force is to be F1, directed along the keel aa

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The boat is to be pulled onto the shore using two ropes. If the resultant force is to be F1, directed along the keel aa as shown, determine the magnitudes of forces T and P acting in each rope and the angle θ of P so that the magnitude of P is a minimum. T acts at θ from the keel as shown.
Given:

θ1 = 30 deg
F1 = 80 lb

F, т

F, т

F,

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