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A mountain climber, in the process of crossing between two cliffs by a rope, pauses to rest. She weighs 535 N. As the drawing shows, she is closer to the left cliff than to the right cliff, with the result that the tensions in the left and right sides of the rope are not the same. Find the tensions in the rope to the left and to the right of the mountain climber.

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I am assuming this is the configuration since she is close to the left one.

Set up X and Y component force balances:

T1 will be left, and T2 will be right.

Y: T1*cos(65) + T2*cos(80) = 535

X: T1*sin(65) = T2*sin(80)

The sines and cosines are switched since the angles were taken from the y axis.

T1 = T2*sin(80)/sin(65)

T2(cos(65)*sin(80)/sin(65) + cos(80)) = 535

T2 = 845.35 N, T1 = 918.573 N

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