A loudspeaker of mass 24.0 {\rm kg} is suspended a distance of h = 2.20 {\rm m} below the ceiling by two cables that make equal angles with the ceiling. Each cable has a length of l = 3.30 {\rm m}.

What is the tension T in each of the cables?
Use 9.80 {\rm m/s}^2 for the magnitude of the acceleration due to gravity.

What equation do I use? How do I solve this???

To solve this problem, we can start by drawing a free body diagram of the loudspeaker.

Let's label the following forces acting on the loudspeaker:
- Tension T1 acting on the left cable
- Tension T2 acting on the right cable
- Weight W acting downwards due to gravity

Since the loudspeaker is in equilibrium, the sum of all the forces acting on it must be zero.

Now let's analyze the forces acting on the loudspeaker:
1. The weight W is acting downwards. Its magnitude can be calculated as W = m * g, where m is the mass and g is the acceleration due to gravity.
2. The tension T1 is acting upwards and to the left at an angle α with the vertical.
3. The tension T2 is acting upwards and to the right at an angle α with the vertical.

Since the angles made by the cables with the ceiling are equal, we can consider them as isosceles triangles. This means that the angles α will each be half of the angle formed between the cables and the ceiling.

Next, let's write the equations for the vertical and horizontal components of the forces:
Vertical forces:
T1 * sin(α) + T2 * sin(α) - W = 0

Horizontal forces:
T1 * cos(α) + T2 * cos(α) = 0

We also know that T1 = T2 because the cables have equal tensions.

Now, to solve for the tensions T1 and T2, we need to rearrange these equations.

1. In the vertical forces equation:
T1 * sin(α) + T2 * sin(α) - W = 0
(T1 + T2) * sin(α) - W = 0
2T * sin(α) - W = 0
2T * sin(α) = W
T * sin(α) = W/2

2. In the horizontal forces equation:
T1 * cos(α) + T2 * cos(α) = 0
(T1 + T2) * cos(α) = 0
2T * cos(α) = 0
T * cos(α) = 0

Now we can solve for T:
T = (W/2) / sin(α)

Given that the mass of the loudspeaker m = 24.0 kg and the acceleration due to gravity g = 9.80 m/s^2, we can calculate W = m * g.

Finally, we can substitute the values into the equation to find the tension T.

So the equation you need to use is T = (W/2) / sin(α), and you can calculate the value of T by finding the weight W and the angle α.

107.5 N