*I really don't know how to get started. I have done lots of the homework, but this one (and a couple of others) are really giving me PROBLEMS.*

In a rescue, a 76.0 kg police officer is suspended by two cables. The left cable is at an angle of 35 degrees below the horizontal, and the right cable is at an agle of 48 degrees below the horizontal.

Find the tension in the left cable.
Answer should be expressed in N.

Find the tension in the right cable.
Answer should be expressed in N.

I need to know what your thinking is on this.

To find the tension in the cables, we need to analyze the forces acting on the police officer. In this scenario, the weight of the officer acts vertically downward, and the tension forces in the cables act at angles below the horizontal.

To get started, we can break down the weight of the officer into its vertical and horizontal components. The vertical component, which is the weight acting in the downward direction, is given by the formula:

Vertical component = Weight * sin(angle)

In this case, the weight is the mass of the officer (76.0 kg) multiplied by the acceleration due to gravity (9.8 m/s^2). We can calculate the vertical component using the above formula for each cable.

Now, let's determine the horizontal component of the weight. The horizontal component is given by the formula:

Horizontal component = Weight * cos(angle)

Again, we can use this formula to calculate the horizontal component for each cable.

Knowing the vertical and horizontal components of the weight, we can apply Newton's second law in the horizontal direction. Since the officer is in equilibrium (no acceleration in the horizontal direction), the sum of the horizontal components of the tension forces must be equal to zero. We can set up the equation:

Left tension * cos(angle_left) + Right tension * cos(angle_right) = 0

We can rearrange this equation to solve for the left tension:

Left tension = - (Right tension * cos(angle_right)) / cos(angle_left)

Finally, we can substitute this value of the left tension into the equation for the vertical direction of Newton's second law:

Vertical component + Left tension * sin(angle_left) + Right tension * sin(angle_right) = 0

We can rearrange this equation to solve for the right tension:

Right tension = - (Vertical component + Left tension * sin(angle_left)) / sin(angle_right)

Remember that the negative sign indicates that the tensions in the cables act in the opposite direction of the officer's weight.

By plugging in the given values for the angles and solving these equations using a calculator or a mathematical software, you can find the tension in the left cable and the tension in the right cable.