The angle between the guy wire and the pole is 46° (rounded to the nearest degree). Solved, using the heights and distances concept of trigonometric ratios.
What is the concept of heights and distances?
The concept of heights and distances is the use of right triangles in real-world examples and solving for missing components using trigonometric ratios in a right triangle.
How to solve the question?
In the question, we are informed that a telephone pole, shown at the top of the next column, is 60 feet tall. A guy wire 86 feet long is attached from the ground to the top of the pole.
We are asked to find the angle between the wire and the pole.
We will use the concept of heights and distances to solve the problem.
We let the pole be AB, of height 60 ft. It is perpendicular to the ground.
We let the guy wire be AC, where C is the point from where the wire is connected on the ground, from a distance from the base of pole B.
The length of the guy wire AC is 86 ft.
We let the angle between the guy wire and the pole, that is, angle BAC be θ.
In the right triangle ABC, we can say that the trigonometric ratio:
cos θ = AB/AC {cos θ = base/hypotenuse}
or, cos θ = 60/86,
or, θ = cos⁻¹(60/86) = 45.8° ≈ 46°.
Therefore, the angle between the guy wire and the pole is 46° (rounded to the nearest degree). Solved, using the heights and distances concept of trigonometric ratios.
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