Answer :
Deepa's observation of angles along with the given distances allows us to use trigonometric functions to calculate the height of the antenna. By solving two tangent equations, we find the heights above her eye level and then determine the height of the antenna itself.
To determine the height of the radio antenna, we can use trigonometric relationships based on the observed angles of elevation. Deepa observes two angles: 35 degrees to the roof of the building (point A) and 41 degrees to the top of the antenna (point B). The horizontal distance to the building is given as 27 meters, and her eye level is 1.69 meters above the ground. Employing the tangent function, which relates the opposite side to the adjacent side in a right-angled triangle, we can write two equations:
- For the height of the point A above her eyes:
tangent(35 degrees) = (Height of A - 1.69 m) / 27 m - For the height of point B above her eyes:
tangent(41 degrees) = (Height of B - 1.69 m) / 27 m
Solving these equations will give us the heights of points A and B above her eye level. To find the height of the antenna, we subtract the height of A from the height of B. The solution involves calculating the heights using a calculator or trigonometry tables, then finding the difference between the two.
