A traffic light weighing 30 pounds is suspended by two wires as shown in the figure below. Find the magnitude |T₁| of the tension in wire AC, and the magnitude /T₂l of the tension in wire AB. (Round your answers to the nearest whole number.) lb lb |T₁|= |T₂| = B T₂ 450! i 60⁰ 000% W T₁

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Section 7.5 question 19
### Problem Statement
A traffic light weighing 30 pounds is suspended by two wires as shown in the figure below. Find the magnitude \( |T_1| \) of the tension in wire AC, and the magnitude \( |T_2| \) of the tension in wire AB. (Round your answer to the nearest whole number.)

#### Given:
- Weight of the traffic light, \( W = 30 \) pounds
- Wires AB and AC form angles of 45 degrees and 60 degrees with the vertical, respectively.

### Diagram Explanation
In the diagram:

- Points A, B, and C represent locations where the wires are attached.
- A traffic light is hanging vertically downward, represented by the weight \( W \).
- There are two wires: one extending from point B to point A (left side of the diagram) and one extending from point C to point A (right side of the diagram).
- Wire \( T_2 \) makes an angle of 45 degrees to the left with the vertical and is attached to point B.
- Wire \( T_1 \) makes an angle of 60 degrees to the right with the vertical and is attached to point C.

The goal is to find the tensions in these wires:

- \( |T_1| \) (tension in wire AC)
- \( |T_2| \) (tension in wire AB)

### Variables to Determine:
- \( |T_1| = \) _____ lb
- \( |T_2| = \) _____ lb
Transcribed Image Text:### Problem Statement A traffic light weighing 30 pounds is suspended by two wires as shown in the figure below. Find the magnitude \( |T_1| \) of the tension in wire AC, and the magnitude \( |T_2| \) of the tension in wire AB. (Round your answer to the nearest whole number.) #### Given: - Weight of the traffic light, \( W = 30 \) pounds - Wires AB and AC form angles of 45 degrees and 60 degrees with the vertical, respectively. ### Diagram Explanation In the diagram: - Points A, B, and C represent locations where the wires are attached. - A traffic light is hanging vertically downward, represented by the weight \( W \). - There are two wires: one extending from point B to point A (left side of the diagram) and one extending from point C to point A (right side of the diagram). - Wire \( T_2 \) makes an angle of 45 degrees to the left with the vertical and is attached to point B. - Wire \( T_1 \) makes an angle of 60 degrees to the right with the vertical and is attached to point C. The goal is to find the tensions in these wires: - \( |T_1| \) (tension in wire AC) - \( |T_2| \) (tension in wire AB) ### Variables to Determine: - \( |T_1| = \) _____ lb - \( |T_2| = \) _____ lb
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