From the figure
#"Upward vertical component of " T_1 =>T_1sin40#
#"Horizontal component of " T_1 =>T_1cos40#
#"Wt of the plank at the mid point"=34xx9.8N#
#"Wt of the man at the point 0.5m from left end"=725N#
#"Leftward horizontal force"=T_3#
#"Upward vertical force on rope at left end" =T_3#
The system is in equlibrium
So considering the equilbrium of forces in horizontal direction, we can write
#T_3=T_1cos40...(1)#
Considering the equilbrium of forces in vertial direction, we can write
#T_2+T_1sin40=(725+34xx9.8)N#
#=>T_2+T_1sin40=1058.2N....(2)#
Cosidering the moments of forces about left end we get
#2xxT_1sin40=0.5xx725+1xx(34xx9.8)#
#=>T_1=695.7/(2sin40)N=541.16N#
Inserting the value of #T_1# in (1)
#T_3=541.16xxcos40=414.55N#
Inserting the value of #T_1# in (2)
#=>T_2+T_1sin40=1058.2N#
#=>T_2+541.16xxsin40=1058.2N#
#=>T_2=1058.2-541.16xxsin40~~710.35N#
