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There is not enough information to answer the question. You need to know the distances between the centres of mass of the plumb bob and the two large masses. The plumb bob may be treated as a point particle, and the distance to the centre of the earth can be approximated by the average radius, but that still leaves the distance to the centre of the mountain.

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Q: How do you calculate the angle of deflection of a plumb line assuming that it is pulled downwards by the mass of the earth 5.89 x 1024 and pulled horizontally by mountain mass of 6.399 x 1015 kg?
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