A guy wire 70ft. long is stretched from the ground of the top of a telephone pole 50ft. high. Find the angle between the wire and the pole?
You have a right-angled triangle, where the hypotenuse and the opposite side to the angle is question is given.
What trig ratio mentioning "opposite" and "hypotenuse" should come to your mind?
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To find the angle between the guy wire and the telephone pole, you can use trigonometry. Specifically, you can use the tangent function.
First, let's draw a diagram to visualize the situation:
/|
/ |
/ | 70ft (guy wire)
/ θ |
/____|
telephone pole (50ft)
In this diagram, the guy wire is represented by a line segment connecting the top of the telephone pole to a point on the ground. The angle between the guy wire and the telephone pole is denoted as θ.
Now, we can set up the trigonometric equation. The tangent of an angle is defined as the ratio of the opposite side to the adjacent side. In this case, the opposite side is the height of the telephone pole (50 ft) and the adjacent side is the distance between the top of the pole and the ground (70 ft).
So, we have:
tan(θ) = opposite/adjacent
= 50ft/70ft
Now, we can find the value of tan(θ) using a scientific calculator or the tangent table. Once you have the value of tan(θ), you can take the inverse tangent to find the angle θ.
To summarize, the angle between the guy wire and the pole is given by θ, where:
θ = arctan(opposite/adjacent)
= arctan(50ft/70ft)
You can use a scientific calculator or an online tool to compute the value of θ.