# vectors

A man weighing 70 kg lies in a hammock whose ropes make angles of
20º and 25º with the horizontal. What is the tension in each rope?

how do you get the following angles for the diagram?

70 corresponds with |T1| (Tension 1)
65 corresponds with |T2| (Tension 2)
45 corresponds with 686 N (9.8 x 70)

The textbook answer is 911.6 N and 879.3 N

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1. Sketch a vector diagram, starting with a vertical AB to represent the 70 kg , with A at the top
Draw AC and BC to meet at C
Angle A = 70° , (90-20)
angle C = 45° , (20+25)
leaving angle B = 65°

using the sine law:
AC/sin 65 = 70/sin45
AC = 70sin65/sin45 = 89.72 kg
BC/sin70 = 70/sin45
BC = 70sin70/sin45 = 93.025 kg

89.72 kg ---> 879.25 N
93.025 kg ---> 911.64 N

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