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?
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To find the angle that the guy wires make with the ground, we can use trigonometry. The angle can be found using the inverse tangent function (arctan).
Let's denote the length of the guy wire (hypotenuse) as "c" and the height of the telephone pole (opposite side) as "a".
In this case, the length of the guy wire (hypotenuse) is 80 feet, and the height of the telephone pole (opposite side) is 65 feet.
Using the right triangle formed by the guy wire, we can apply the trigonometric identity: tangent(theta) = opposite/adjacent. Here, the opposite side is the height of the pole, and the adjacent side is the distance from the base of the pole to where the guy wire is anchored.
So, in this case, we have tangent(theta) = a/c. Plugging in the values, we get tangent(theta) = 65/80.
Now, to find the angle (theta), we can take the inverse tangent (arctan) of both sides:
theta = arctan(65/80)
Using a calculator, we can find the approximate value of arctan(65/80). Rounding the result to the nearest degree will give us the angle that the guy wires make with the ground.
Draw a diagram, and it will be clear that the pole is opposite to the angle the wire makes with the ground.
Since the wire is at an angle, it is also the hypotenuse of the right triangle.
The ratio
sin(θ)=opposite/hypotenuse
=65/80
is what you need to find the angle using θ=sin-1(65/80).
Post your answer for a check if you wish.