Consider the 667 N weight held by two cables shown below. The left-hand cable had tension 890 N and makes an angle of è with the wall. The right-hand cable had tension 960 N and makes an angle of è1 with the ceiling.

a) What is the angle è1 which the right- hand cable makes with respect to the ceiling? Round up to four significant digits. Express unit as ”degrees”.

b) What is the angle è which the left-hand cable makes with respect to the wall? Round up to four significant digits. Express unit as ”degrees”.

The process has stumbled me for a while, but am certain that I need to use sin^2 + cos^2=1 somewhere along the way. I appreciate your help!

To solve this problem, we can use the concept of tension in cables and trigonometry. Let's consider the forces acting on the weight.

a) To find angle è1, we need to use the tension in the right-hand cable (960 N) and the force due to gravity acting on the weight (667 N). From the information given, we know that the weight is in equilibrium, meaning that the net force acting on it is zero.

The vertical component of the tension in the right-hand cable (960 N) balances the weight (667 N). So, we can set up an equation:

Tension * sin(è1) = Weight

960 N * sin(è1) = 667 N

To solve for angle è1, we rearrange the equation:

sin(è1) = 667 N / 960 N

Now, we can take the inverse sine (or arcsine) of both sides to find the angle è1:

è1 = arcsin(667 N / 960 N)

Using a calculator, we find that è1 is approximately 40.3737 degrees when rounded to four significant digits.

b) Similarly, to find angle è, we use the tension in the left-hand cable (890 N) and the weight (667 N).

Tension * sin(è) = Weight

Using the given tension (890 N), we can set up the equation:

890 N * sin(è) = 667 N

Rearranging the equation:

sin(è) = 667 N / 890 N

Now, we can find angle è by taking the inverse sine:

è = arcsin(667 N / 890 N)

Using a calculator, we find that è is approximately 48.1996 degrees when rounded to four significant digits.

In summary:

a) The angle è1 is approximately 40.3737 degrees.
b) The angle è is approximately 48.1996 degrees.

Remember, when solving problems like these, it's always a good idea to draw a diagram and carefully label all the given information. Then, apply relevant equations and trigonometric relationships to find the desired quantities.