Consider the 59 N weight held by two cables The left-hand cable is horizontal.

What is the tension in the cable slanted
at an angle of 51◦? Answer in units of N.

What is the tension in the horizontal cable?
Answer in units of N.

Start with the vertical forces. Weight, downward. THe vertical component of the right hand must equal that.

To find the tension in the slanted cable, we can use trigonometry. Let's call the tension in the slanted cable T_slanted. Since the left-hand cable is horizontal, there is no vertical component of tension in that cable.

To find T_slanted, we need to consider the vertical and horizontal components of the weight being supported. The vertical component is given by the weight multiplied by the sine of the angle between the weight and the vertical direction. In this case, the angle is 51°. So, the vertical component of the weight is 59 N * sin(51°).

Since the vertical component of the weight is balanced by the tension in the slanted cable, we can say T_slanted is equal to the vertical component of the weight. Therefore, T_slanted = 59 N * sin(51°).

To find the tension in the horizontal cable (T_horizontal), we need to consider the horizontal component of the weight being supported. The horizontal component is given by the weight multiplied by the cosine of the angle between the weight and the horizontal direction. In this case, the angle is 51°. So, the horizontal component of the weight is 59 N * cos(51°).

Since the horizontal component of the weight is balanced by the tension in the horizontal cable, we can say T_horizontal is equal to the horizontal component of the weight. Therefore, T_horizontal = 59 N * cos(51°).

Now we can calculate the tensions in both cables.

T_slanted = 59 N * sin(51°) = [calculate the value]

T_horizontal = 59 N * cos(51°) = [calculate the value]

Keep in mind that the values of T_slanted and T_horizontal will depend on the specific calculations. You can use a scientific calculator or trigonometric functions in a programming language to obtain the accurate values.