SOLUTION: A 12 ft guy wire is attatched to a telephone pole 10.5 ft from the top of the pole. If the wire forms a 52 degree angle with the ground, how high is the telephone pole?

Algebra ->  Trigonometry-basics -> SOLUTION: A 12 ft guy wire is attatched to a telephone pole 10.5 ft from the top of the pole. If the wire forms a 52 degree angle with the ground, how high is the telephone pole?      Log On


   

Question 592809: A 12 ft guy wire is attatched to a telephone pole 10.5 ft from the top of the pole. If the wire forms a 52 degree angle with the ground, how high is the telephone pole?
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
If we knew the distance from the ground up to where the wire is attached to the pole, then we could find the total height of the pole by adding that distance to the 10.5 distance from the wire to the top of the pole. So we need to find the distance from the ground up to where the wire is attached to the pole.

To find the distance from the ground up to where the wire is attached to the pole...
  1. Draw a right triangle with horizontal and vertical legs. The horizontal side is the ground, the vertical side is the pole and the hypotenuse is the wire.
  2. Add the given facts to the diagram:
    • Mark the angle between the ground and the wire as 52 degrees.
    • Label the wire as 12 ft. long
  3. Assign a variable to the desired number. We want the vertical side so let's label it as "x".
  4. At this point there are two possibilities:
    • The variable is a side and you know the other two sides of the right triangle. In this case you can simply use the Pythagorean Theorem to find the 3rd side.
    • In any other case:
      1. Pick an acute angle and two sides. One of these must the the variable/unknown and the other two should be known numbers. In your problem you must pick the vertical side (the unknown), the hypotenuse (known) and the 52 degree angle (known).
      2. Select an appropriate trig ratio that involves the three selected values. Since the vertical side is opposite to the angle, then we want a ratio that involves the opposite side and the hypotenuse. This means either sin (opposite/hypotenuse) or csc (hypotenuse/opposite) should be used. (I recommend using sin since your calculator has sin and inverse sin buttons but not any csc buttons.)
      3. Write and solve the equation for the selected ratio.
        sin%2852%29+=+x%2F12
        So solve for x we'll start by multiplying each side by 12:
        12%2Asin%2852%29+=+x
        This is an exact expression for the desired distance. So and exact answer for the height of the pole would be {{12*sin(52) + 10.5}}}. If you want/need a decimal approximation, get out your calculator and ask it for sin(52). (Make sure your calculator is set for degree mode!) Now we have:
        12%2A0.7880+=+x
        which simplifies to
        9.4561+=+x
        So the approximate height of the pole is: 9.4561 + 10.5 = 19.9561 ft.