Consider the 667 N weight held by two cables shown below. The left-hand cable had tension 890 N and makes an angle of θ with the wall. The right-hand cable had tension 960 N and makes an angle of θ1 with the ceiling.

a) What is the angle θ1 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 θ 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 principles of trigonometry and the equation you mentioned, sin^2 + cos^2 = 1.

a) To find the angle θ1, we can use the information given. The right-hand cable has a tension of 960 N and makes an angle of θ1 with the ceiling. We can consider the weight being held by the cables as the vertical component of the tension in both cables.

The vertical component of the tension in the right-hand cable is given by T1sinθ1, where T1 is the tension in the right-hand cable and θ1 is the angle it makes with the ceiling.

Given that the weight being held is 667 N, we can write the equation:

T1sinθ1 = 667

Now, let's use the equation sin^2 + cos^2 = 1 to relate the angles θ and θ1:

sinθ = cos(90 - θ) = cos(θ1)

Now, we can substitute sinθ with cos(θ1) in the equation above:

T1cos(θ1) = 667

Rearranging the equation to solve for θ1, we have:

cos(θ1) = 667 / T1

Taking the inverse cosine (cos^-1) of both sides, we get:

θ1 = cos^-1(667 / T1)

Using the given tension T1 = 960 N, we can substitute the values and solve for θ1. Make sure to round the angle to four significant digits and express it in degrees.

b) To find the angle θ, the left-hand cable's tension is given as 890 N and forms an angle θ with the wall. Using the same process, we can write:

Tsinθ = 667

Applying the relationship sinθ = cos(90 - θ) = cos(θ1) from the previous equation, we get:

Tcos(θ) = 667

Rearranging and solving for θ, we have:

θ = cos^-1(667 / T)

Substituting the given tension T = 890 N, we can solve for θ, rounding to four significant digits and expressing in degrees.

By following these steps, you should be able to find the angles θ1 and θ using the given tension values and the weight being held by the cables.