Consider the 665 N weight held by two cables

The left-hand cable had tension T2 and makes an angle of 43◦ with the ceiling. The right-hand cable had tension T1
and makes an angle of 48◦ with the ceiling.
What is the tension in the cable
T1 slanted at an angle of 48◦?
Answer in units of N

sum of vertical forces is zero.

665-T1*sin48-T2*sin43=0
sum of horizontal forces is zero
T1*cos48-T2*cos43=0

solve this system of two equations, two unknowns.

Answer is T1=23.33N and T2=67.56N

T1=20.33 and T2=60.56

To find the tension in the cable T1 slanted at an angle of 48◦, we can use the concept of equilibrium. In equilibrium, the sum of all the forces acting on an object is equal to zero.

Let's break down the given information:
- Weight of the object = 665 N (acting downwards)
- Left-hand cable (Cable 2): Angle with the ceiling = 43°
- Right-hand cable (Cable 1): Angle with the ceiling = 48°

Since the object is in equilibrium, the vertical component of the tension in both cables must balance the weight of the object. The horizontal components of the tensions cancel each other out.

Let's start with the vertical components:
- Vertical component of T1: T1 * sin(48°)
- Vertical component of T2: T2 * sin(43°)

The sum of the vertical components of these tensions should equal the weight of the object:
T1 * sin(48°) + T2 * sin(43°) = 665 N

Now, to find the tension in the cable T1 (T1 slanted at an angle of 48◦), we need to rearrange the equation to solve for T1:
T1 = (665 N - T2 * sin(43°)) / sin(48°)

Unfortunately, the value of T2 is not specified in the question, so we cannot determine the exact tension in the cable T1. However, if you have the value of T2, you can substitute it into the equation and solve for T1 using a scientific calculator or any software that can evaluate trigonometric functions.