### Problem StatementFind the tension in each of the three cables (in N) supporting the traffic light if it weighs \(4.67 \times 10^2\) N.### Diagram ExplanationThe diagram illustrates a traffic light supported by three cables:1. **Cable 1**: Makes an angle of \(41.0^\circ\) with the horizontal.2. **Cable 2**: Makes an angle of \(63.0^\circ\) with the horizontal.3. **Cable 3**: Hangs vertically downward and directly supports the traffic light.The weight of the traffic light, \(w\), is given as 467 N, directed downwards.### Necessary CalculationsTo compute the tensions \(T_1\), \(T_2\), and \(T_3\) in the cables:1. **Equilibrium in the vertical direction**: - Summation of vertical components of the tensions \(T_1\) and \(T_2\) should equal the weight supported by them minus \(T_3\).2. **Equilibrium in the horizontal direction**: - The horizontal components of tensions \(T_1\) and \(T_2\) must balance each other.#### Equations- \(T_1 \cos(41.0^\circ) + T_2 \cos(63.0^\circ) = 0\)- \(T_1 \sin(41.0^\circ) + T_2 \sin(63.0^\circ) = 467 \text{ N}\)- \(T_3 = \text{component supporting the vertical weight}\)### Input Fields for Solution\[ T_1 = \boxed{} \text{ N} \]\[ T_2 = \boxed{} \text{ N} \]\[ T_3 = \boxed{} \text{ N} \]

Name: ### Problem StatementFind the tension in each of the three cables (in
Uploaded: 2024-03-20T06:56:46.000Z
Channel: Bartleby
Description: ### Problem StatementFind the tension in each of the three cables (in N) supporting the traffic light if it weighs \(4.67 \times 10^2\) N.### Diagram ExplanationThe diagram illustrates a traffic light supported by three cables:1. **Cable 1**: Makes