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Can anyone help me?
Question 3, May/June 2011 Paper 41.
Refer to the above diagram and solve the horizontal and the vertical components of forces.
Horizontal Component:
T cos θ + T sin θ = 15.5
T cos θ = 15.5 - T sin θ
Vertical Component:
T cos θ + 8 = T sin θ
15.5 - T sin θ + 8 = T sin θ
23,5 = 2 T sin θ
11.75 = T sin θ
Therefore, T sin θ = 11.75~12
Put back this value of 'T sin θ' in the equation 'T cos θ = 15.5 - T sin θ'.
T cos θ = 15.5 - T sin θ
T cos θ = 15.5 - 12
T cos θ = 3.5.
Therefore, T cos θ = 3.5,
To find the value of θ, use the formula 'tan θ = opposite/adjacent'.
tan θ = opposite/adjacent
tan θ = (T sin θ) / (T cos θ)
tan θ = 12/3,5
θ = 73.73o