Final answer:
To find the height of the hill, trigonometric principles are applied using the provided angle of elevation to the bottom of the antenna and possibly the angle it subtends. However, since the angle subtended by the antenna is unspecified in the question, the exact height cannot be determined without additional information.
Step-by-step explanation:
The student is asking how to find the height of a hill given the angle of elevation to the bottom of an antenna that is known to be 110 feet tall and the angle it subtends from the point on the ground. To solve this problem, one would use trigonometric relationships. Considering the angle of elevation to be 30 degrees to the bottom of the antenna, we can represent the situation with a right-angle triangle where the hill's height is the opposite side and the point on the ground to the base of the hill is the adjacent side. The tangent of 30 degrees is equal to the opposite side (height of the hill) divided by the adjacent side (distance to the hill from the person).
However, there might be an error in the original question as it mentions that the angle subtended by the antenna is '2' which does not specify a unit. We would need to know this angle in degrees, radians, or another unit of measurement to appropriately calculate the height of the hill.
To answer the question as it's given, we will assume there is a typo and disregard the mention of the antenna subtending an angle of '2'. Using only the 30 degrees angle of elevation, one can set up the following equation using the tangent function:
tan(30 degrees) = height of the hill / distance to the hill
Since we need to find just the height of the hill and do not have the distance, we are unable to calculate the exact height without additional information. If the actual height of the hill is required, please double-check the question for any missing information or clarifications on the angle subtended by the antenna.