An electric pole is supported to stand vertically on a level ground by a tight wire. The wire is pegged at a distance of 6 meters from the foot of the pole as shown. The angle that the wire makes the ground is three times the angle it makes with the pole. Calculate the length of wire to the nearest centimeter.
anser
Plzz I need the answer to the above quiz
To solve this problem, we can use trigonometric ratios.
Let's denote the angle between the wire and the ground as x, and the angle between the wire and the pole as y.
From the problem statement, we know that the angle x is three times the angle y.
Now, let's consider the right-angled triangle formed by the wire, the ground, and the pole. The side opposite to angle x is the height of the pole, and the side adjacent to angle x is the distance between the pole and the point where the wire is pegged into the ground.
Using trigonometric ratios, we have:
tangent(x) = opposite/adjacent
Since the height of the pole is the opposite side and the distance from the pole to the wire peg is the adjacent side, we have:
tangent(x) = height/6
Now, from the problem statement, we know that x = 3y. Therefore, we can write:
tangent(3y) = height/6
Using the property of tangent function (tangent(3y) = 3 * tangent(y)), we have:
3 * tangent(y) = height/6
Simplifying further, we get:
tangent(y) = height/18
Now, we can use the inverse tangent function (arctan) to find the value of y:
y = arctan(height/18)
Next, we can use the sine function to relate the angle y to the length of the wire. The sine of angle y is equal to the height of the pole divided by the length of the wire:
sine(y) = height/wire_length
Rearranging the equation, we have:
wire_length = height/sine(y)
Now, we can substitute the value of y from the previous equation into this equation to get the wire length in terms of the height of the pole:
wire_length = height/sine(arctan(height/18))
Finally, we need to determine the value of the height of the pole. Since we know that the angle x is three times the angle y, we can write:
x = 3y
Using the relationship between the angles of a triangle (180 degrees), we have:
x + y + 90 = 180
Substituting x = 3y:
3y + y + 90 = 180
4y = 90
y = 22.5 degrees
Now, we can substitute the value of y back into the equation for wire length:
wire_length = height/sine(arctan(height/18))
Wire length ≈ height/sine(arctan(height/18))
Now, to find the length of the wire, we need the actual height of the pole. Unfortunately, the problem statement doesn't provide that information. Without the height of the pole, we cannot determine the length of the wire accurately.