Question

An audio speaker that weighs 50 pounds hangs from the ceiling of a restaurant from two cables(45 degrees left and 35 degrees right). To two decimal places, what is the tension in the two cables?

Answer 1

Answer to Question #88642 – Math – Trigonometry

Question

An audio speaker that weighs 50 pounds hangs from the ceiling of a restaurant from two cables (45 degrees left and 35 degrees right). To two decimal places, what is the tension in the two cables?

Solution

As given an audio speaker that weight 50 pounds hangs from ceiling of restaurant from cables as shown in figure below.

Let T1 be the tension in cable which make 45 degree and T2 is the tension in cable which make 35-degree angle.

Now, the sum of two vertical components of tensions must be equal to 50 pounds and horizontal component of tensions must be equal and opposite.

Vertical component of Tension $T1V = T1 \sin 45{}^\circ$

Vertical component of Tension $T2V = T2 \sin 35{}^\circ$

Horizontal component of Tension $T1H = T1 \cos 45{}^\circ$

Horizontal component of Tension $T2H = T2 \cos 35{}^\circ$

$$T1 \sin 45{}^\circ + T2 \sin 35{}^\circ = 50 \quad (i)$$ $$T1 \cos 45{}^\circ = T2 \cos 35{}^\circ \quad (ii)$$

Solving (i) and (ii)

$$T1 = \frac{T2 \cos 35{}^\circ}{\cos 45{}^\circ}$$ $$T1 = 1.16 T2$$ $$1.16 T2 \sin 45{}^\circ + T2 \sin 35{}^\circ = 50$$ $$T2(.82 + .57) = 50$$ $$T2 = 35.97 \text{(pounds)}$$ $$T1 = 1.16 * 35.97 = 41.72 \text{ (pounds)}.$$

**Answer:**

$T1 = 41.72$ pounds and $T2 = 35.97$ pounds.

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