Final answer:
The tension in the slanted cable, which forms a 45° angle with the horizontal, is calculated to be 66.4 N to support a 47 N weight.
Step-by-step explanation:
To determine the tension in the slanted cable, we need to use the principles of static equilibrium, where the sum of all forces in the horizontal and vertical directions equals zero. The 47 N weight is only supported by the vertical component of the tension in the slanted cable, since the left-hand cable is horizontal and thus cannot support any of the weight's vertical load. Given that the slanted cable forms a 45° angle with the horizontal, its tension can be found by dividing the weight by the cosine of the angle for the horizontal component or the sine of the angle for the vertical component (which are equal at 45°).
ΣFy = Tslantedsin(45°) - 47 N = 0
Tslanted = 47 N / sin(45°)
Tslanted = 47 N / (√2/2)
Tslanted = 66.4 N
Therefore, the tension in the cable slanted at a 45° angle is 66.4 N.