A traffic light weighing 15 pounds is suspended by two cables (see figure).Find the tension in each cable if θ₁ = 40° and θ₂ = 35°.Approximate the answers to one decimal place. A)T_L = 12.7 lb;TR = 12.7 lb B)T_L = 11.9 lb;TR = 11.9 lb C)T_L = 11.9 lb;TR = 12.7 lb D)T_L = 12.7 lb;TR = 11.9 lb E)T_L = 13.7 lb;TR = 12.9 lb

Question

Quizplus · Accepted Answer

Using the law of sines, we can write:

TS1U1B1/ sin(40°) = TR/ sin(145°)
TS1U1B1/ sin(35°) = TR/ sin(125°)

Solving for TS1U1B1 and TR, we get:

TS1U1B1 = sin(40°) sin(125°) TR / sin(145°) sin(35°)

TR = sin(35°) sin(145°) TS1U1B1 / sin(125°) sin(40°)

Plugging in the given values and simplifying, we get:

TS1U1B1 ≈ 12.7 lb

TR ≈ 11.9 lb

Therefore, the best choice is (D), which gives the correct values for both tension forces.

A Traffic Light Weighing 15 Pounds Is Suspended by Two