Find the tension T2 of the box hanging from the rope if 1 = 25°, 2 = 65°, T1 = 60.58 newtons, and W = 143.4 newtons answer please

To find the tension T2 of the box hanging from the rope, we can use the method of resolving forces. Let's break down the problem step by step:

1. Draw a diagram: Draw a diagram representing the situation. Label the angles and the given forces.

T1 = 60.58 N W = 143.4 N
|_ 2 _|
|_ _|
|_ _|
1

2. Resolve the forces: Resolve the given forces into their x and y components. For this, we will use trigonometry.

T1 can be split into its x and y components as follows:
Tx1 = T1 * cos(1) (horizontal component)
Ty1 = T1 * sin(1) (vertical component)

W can be split into its x and y components as follows:
Wx = W * cos(2) (horizontal component)
Wy = W * sin(2) (vertical component)

3. Determine the vertical forces: The vertical forces in equilibrium should be equal. So, we have:
T2 + Wy + Ty1 = 0

4. Calculate T2: Rearrange the equation to solve for T2:
T2 = -Wy - Ty1

Substitute the values into the equation:
T2 = - (W * sin(2)) - (T1 * sin(1))

Substituting the given values, we get:
T2 = - (143.4 N * sin(2)) - (60.58 N * sin(1))

5. Calculate T2: Use a calculator to evaluate the expression and find the value of T2.

T2 ≈ -29.76 N

Therefore, the tension T2 of the box hanging from the rope is approximately -29.76 newtons. Note that the negative sign indicates that the tension is in the opposite direction of the weight.

D the answer is D