Answer:
B. 171 N
Explanation:
The equation of the forces along the horizontal and vertical directions are:
Horizontal:
[tex]T_2 cos 62^{\circ} = T_1 cos 20^{\circ}[/tex] (1)
Vertical:
[tex]T_1 sin 20^{\circ} + T_2 sin 62^{\circ} = W[/tex] (2)
Where W = 180 N is the weight of the box.
From (1),
[tex]T_2 \frac{cos 62^{\circ}}{cos 20^{\circ}} = T_1 [/tex]
Substituting into (2),
[tex](T_2 \frac{cos 62^{\circ}}{cos 20^{\circ}}) sin 20^{\circ} + T_2 sin 62^{\circ} = W\\T_2 (cos 62^{\circ} tan 20^{\circ}+sin 62^{\circ})=W\\T=\frac{W}{cos 62^{\circ} tan 20^{\circ}+sin 62^{\circ}}=171 N[/tex]
