A surveyor stands 200m from the base of a tower on which an Ariel stands. He measures the angle of elevation to the top and bottom of the Ariel as 58 degree and 56 degree. Find the height of the Ariel.
Ariel is a person's name
An aerial is an antenna
recall the definition of tan(x) and you will see that the aerial's height is
200tan58° - 200tan56°
To find the height of the Ariel, we can use the concept of trigonometry and the given angle of elevation measurements.
Let's assume the height of the Ariel is represented by "h" meters.
Since the surveyor is standing 200m away from the base of the tower, we can consider this distance as the base of a right triangle. The height of the tower (which includes the Ariel) will be the opposite side, and the distance of the surveyor from the base will be the adjacent side. The angle of elevation to the top of the Ariel will be the angle opposite to the height.
Therefore, we can define the following trigonometric relationship:
tan(angle) = opposite / adjacent
For the first angle of elevation:
tan(58°) = h / 200m
To isolate the height (h), we rearrange the equation:
h = tan(58°) * 200m
Next, we'll calculate the height using a scientific calculator or math software:
h ≈ tan(58°) * 200m
h ≈ 2.1445 * 200m
h ≈ 428.90m
So, the height of the Ariel is approximately 428.90 meters.