a guy wire 27.0m long is stretched from the ground to the top of a telephone pole 22.0m high. find the angle between the wire and pole
sin angle = 22/27
To find the angle between the wire and the pole, you can use trigonometric functions. In this case, we will use the tangent function.
Let's label the angle between the wire and the ground as θ.
According to the given information, the opposite side of the angle θ is the height of the pole, which is 22.0m, and the adjacent side is the length of the guy wire, which is 27.0m.
Applying the tangent function:
tan(θ) = opposite / adjacent
tan(θ) = 22.0m / 27.0m
Now, we can calculate the angle θ by taking the arctan (inverse tangent) of both sides of the equation:
θ = arctan(22.0m / 27.0m)
Using a scientific calculator or an online calculator, you can input the above expression to find the angle. The result is approximately 39.82 degrees.
Therefore, the angle between the wire and the pole is approximately 39.82 degrees.
To find the angle between the guy wire and the pole, you can use trigonometry. Specifically, you can use the tangent function.
Let's call the angle between the wire and the pole "θ" (theta). From the given information, we have the length of the guy wire (27.0m) and the height of the pole (22.0m).
Using the tangent function, we can set up the following equation:
tan(θ) = Opposite / Adjacent
In this case, the opposite side is the height of the pole (22.0m) and the adjacent side is the length of the guy wire (27.0m). Plugging these values into the equation:
tan(θ) = 22.0m / 27.0m
Now, to find the angle θ, we need to take the inverse tangent (also called arctan or tan^(-1)) of both sides of the equation:
θ = tan^(-1)(22.0m / 27.0m)
Using a calculator or a mathematical software, you can find the inverse tangent:
θ ≈ 41.82 degrees
Therefore, the angle between the guy wire and the pole is approximately 41.82 degrees.