Guy wires 80 feet long support a 65 foot tall telephone pole. To the nearest degree, what angle will the wires make with the ground?
sinθ = 65/80
θ = arcsin(65/80)
θ = 54.34°
solve A Flag Pole Has A Height Of 16 Yards. It Will Be Supported By Three Cables, Each Of Which Is Attached To The Flagpole At A Point 4 Yards Below The Top Of The Pole And Attached To The Ground At A Pole. Find the total number of feet of cable that will be required
This problem has some missing information. You know that the pole is 16 feet high, and the wires connect 12 feet up (16-4=12). If you found the length from the bottom of the pole to the grounding point, you could use the equation 12^2+X^2=L^2 with x standing for the length of the bottom of the pole to the grounding point. Another way you could figure this out is by finding the angle of the cable (A) coming up from the ground with equation Sin(A)=12/X with x being the length of the cable that you are trying to find.
To find the angle the guy wires make with the ground, we can use trigonometry. Since we have a right triangle formed by the guy wires, the telephone pole, and the ground, we can use the tangent function.
The tangent of an angle is defined as the opposite side divided by the adjacent side. In this case, the opposite side is the height of the telephone pole (65 feet) and the adjacent side is half the length of the guy wires (80 feet / 2 = 40 feet).
So, the tangent of the angle can be calculated as:
tan(θ) = opposite / adjacent
tan(θ) = 65 / 40
Now, to find the value of the angle θ, we can take the inverse tangent (also known as arctan or tan^(-1)) of both sides:
θ = arctan(tan(θ))
θ = arctan(65 / 40)
Using a calculator, the value of arctan(65 / 40) is approximately 58.28 degrees.
Therefore, the angle the guy wires make with the ground, to the nearest degree, is 58 degrees.