SOLUTION: A telegraph pole is supported by a guy wire which exerts a 1kn pull on the top of the pole. The guy wire makes an angle of 42 degrees with the pole. Determine the horizontal and v

Algebra ->  Trigonometry-basics -> SOLUTION: A telegraph pole is supported by a guy wire which exerts a 1kn pull on the top of the pole. The guy wire makes an angle of 42 degrees with the pole. Determine the horizontal and v      Log On


   

Question 626426: A telegraph pole is supported by a guy wire which exerts a 1kn pull on the top of the pole. The guy wire makes an angle of 42 degrees with the pole. Determine the horizontal and vertical components of the pull on the pole.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
You might want to draw a diagram. Draw a right triangle with horizontal and vertical legs. The vertical leg is the telephone pole, the horizontal leg is the ground and the hypotenuse is the guy wire. Label the guy wire with a 1 to represent the force on the wire. And label the angle between the wire and the pole as 42 degrees.

To find the horizontal component of the pull, we will use sin because
  • sin is opposite over hypotenuse
  • the horizontal side is opposite to the angle we know
  • we know the hypotenuse
The equation we will use is:
sin%2842%29+=+x%2F1
which simplifies to
sin(42) = x
Just use your calculator to find a decimal approximation for the horizontal component.

We will use similar logic to find the vertical component, except we will use cos since cos is adjacent over hypotenuse and the vertical side is adjacent to the angle we know.
cos%2842%29+=+y%2F1
or just
cos(42) = y
Again, just use your calculator to find a decimal approximation for the vertical component.