Find the height of an antenna knowing that at a distance of 18 m the top of the antenna is seen at an angle of 30%
We can use trigonometry to solve this problem.
Let's assume the height of the antenna is h meters.
From the given information, we can form a right triangle with the vertical height h, the distance of 18 m, and the angle of 30 degrees.
By using the definition of tangents, we know that the tangent of an angle is equal to the ratio of the opposite side to the adjacent side.
In this case, the tangent of 30 degrees is equal to the height divided by the distance:
tan(30) = h/18
The tangent of 30 degrees can be calculated as:
tan(30) = 0.577
Now we can solve for h:
0.577 = h/18
Multiply both sides by 18 to isolate h:
h = 0.577 * 18 = 10.386
Therefore, the estimated height of the antenna is approximately 10.386 meters.
To find the height of the antenna, we can use trigonometry. Let's consider the situation:
Let h be the height of the antenna.
Given that the top of the antenna is seen at an angle of 30 degrees.
We can set up a right triangle with the following information:
Opposite side: height of the antenna (h)
Adjacent side: distance from the observer to the base of the antenna (18 m)
Angle: 30 degrees
Using the tangent function:
tan(30°) = Opposite side / Adjacent side
tan(30°) = h / 18
To find the height (h), we can rearrange the equation:
h = tan(30°) * 18
h ≈ 10.392 * 18
h ≈ 187.056
Therefore, the height of the antenna is approximately 187.056 meters.