Deepa is trying to find the height of a radio antenna on the roof of a local building. She stands at a horizontal distance of 27 meters from the building. The angle of elevation from her eyes to the roof (point A) is 35 degrees, and the angle of elevation from her eyes to the top of the antenna (point B) is 41 degrees. If her eyes are 1.69 meters from the ground, find the height of the antenna (the distance from point A to point B). Round your answer to the nearest meter if necessary.

A) h
B) 2h
C) 3h
D) 4h

In this scenario, Deepa aims to determine the height of the radio antenna positioned atop a building. Utilizing principles of trigonometry, she measures the angles of elevation from her eyes to distinct points: the building's roof (point A) and the top of the antenna (point B). Given a horizontal distance of 27 meters between herself and the building, Deepa initiates her calculations.

Initially, she computes the height of the building using the tangent function with the angle of elevation at point A, which is 35 degrees. Plugging this angle and the horizontal distance into the tangent formula, she derives an approximate height of 16.2 meters for the building. Subsequently, she employs the same methodology for point B, where the angle of elevation is 41 degrees. This calculation reveals an approximate height of 7.8 meters from point A to point B, representing the height of the antenna from the building's rooftop.

To determine the overall height of the antenna, Deepa sums the heights obtained for the building and the antenna's vertical distance from the rooftop. Consequently, the total height of the antenna is approximately 16 meters. This comprehensive approach allows Deepa to accurately ascertain the height of the radio antenna, facilitating efficient planning and implementation of any necessary adjustments or installations. Therefore, the correct option is h (Option A).