Answer:
Tension in the 55 degree cable = 110.56 N
Tension in the 28.5 degree cable = 72.16 N
Explanation:
Decompose the two tensions T1 (on left cable) and T2(on right cable) in vertical and horizontal components using trigonometric functions sine and cosine. Then balance the forces in the vertical and in the horizontal as shown below:
Horizontal components acting on net horizontal force:
T1 cos(55) =T2 cos(28.5)
then T1 = T2 (cos(28.5) / cos(55))
Vertical components acting on net vertical force:
T1 sin(55) + T2 sin(28.5) = 125
Now replace T1 with T2 (cos(28.5) / cos(55)) in the last equation:
T2 (cos(28.5) * sin(55)/ cos(55)) + T2 * sin(28.5) = 125
T2 ( cos(28.5) * tan(55) + sin(28.5)) = 125
solving for T2 we get: 72.16 N
now we use this T2 result in the substitution equation:
T1 = T2 (cos(28.5) / cos(55))
T1 = 110.56 N
