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, you can indeed use the trigonometric identity sin^2(theta) + cos^2(theta) = 1. Here's how you can apply it to find the angles è and è1:
a) Let's start with the right-hand cable. We know that the tension in the cable is 960 N. Let's assume the angle it makes with the ceiling is è1.
Using the given information, we can set up the following equation:
960 N = Tension * cos(è1)
Now, we can rearrange this equation to solve for cos(è1):
cos(è1) = 960 N / Tension
To find the angle è1, we can take the inverse cosine (cos^-1) of both sides of the equation:
è1 = cos^-1(960 N / Tension)
Plugging in the given values, we get:
è1 = cos^-1(960 N / 960 N)
Since cos^-1(1) = 0, the angle è1 is 0 degrees.
b) Now let's move on to the left-hand cable. We know the tension in the cable is 890 N, and the angle it makes with the wall is è.
Using the given information, we can set up the following equation:
890 N = Tension * sin(è)
Now, rearrange this equation to solve for sin(è):
sin(è) = 890 N / Tension
To find the angle è, we can take the inverse sine (sin^-1) of both sides of the equation:
è = sin^-1(890 N / Tension)
Plugging in the given values, we get:
è = sin^-1(890 N / 890 N)
Since sin^-1(1) = 90 degrees, the angle è is 90 degrees.
Therefore, the answers to the questions are:
a) The angle è1 which the right-hand cable makes with respect to the ceiling is 0 degrees.
b) The angle è which the left-hand cable makes with respect to the wall is 90 degrees.
Remember to round up to four significant digits as requested.