The 665 N weight held by two cables. The left-hand cable had tension T2 and makes an angle of 43 degrees with the ceiling. The right-hand cable had tention t1 and makes an angle of 48 degrees with the ceiling. What is the tension in the cable labeled t1 slanted at an angle of 48 degrees?

Solve the following two equations for T1 and T2.

T1 cos48 + T2 cos43 = 665
(vertical force balance)
T1 sin48 -T2 cos48 = 0
(horizontal force balance)

To solve this problem, we can start by analyzing the forces acting on the weight.

Let's break down the forces along the vertical and horizontal directions:

Vertical forces:
1. The weight itself, which is equal to 665 N and acting downward.

Horizontal forces:
1. The left-hand cable (T2) exerts a horizontal force in the left direction.
2. The right-hand cable (T1) exerts a horizontal force in the right direction.

Next, we can calculate the vertical and horizontal components of the tension forces.

For the left-hand cable (T2):
The weight is acting straight downward, while the cable is at an angle of 43 degrees with the ceiling. Therefore, the vertical component of T2 is given by:
Vertical component of T2 = T2 * cos(43°)

The horizontal component of T2 is given by:
Horizontal component of T2 = T2 * sin(43°)

Similarly, for the right-hand cable (T1):
The weight is acting straight downward, while the cable is at an angle of 48 degrees with the ceiling. Therefore, the vertical component of T1 is given by:
Vertical component of T1 = T1 * cos(48°)

The horizontal component of T1 is given by:
Horizontal component of T1 = T1 * sin(48°)

Since the weight is balanced, the sum of the vertical components of T1 and T2 must equal the weight:
Vertical component of T1 + Vertical component of T2 = weight

Plugging in the given values:
T1 * cos(48°) + T2 * cos(43°) = 665 N

We need to solve this equation to find the value of T1.