Question
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%
Answers
GPT 3.5
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.
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.