Final answer:
To find the height of the television tower, we utilize trigonometric functions based on the given angles of elevation and depression with respect to David's window, using the distance from his house to the tower as the adjacent side length in the calculations.
Step-by-step explanation:
The student has provided information that can be used to solve for the height of the television tower using trigonometry. Since David's house is 16 meters away from the tower, this distance forms the adjacent side of two right-angle triangles - one formed by the angle of elevation and the other by the angle of depression. To find the height of the tower, we can use the tangent function, which is the ratio of the opposite side to the adjacent side in a right-angle triangle.
Let's call the height from the ground to David’s window h1, and the height from David’s window to the top of the tower h2. The total height of the tower is then h = h1 + h2. We can write two equations based on the tangent of the given angles:
- tan(24°) = h1 / 16
- tan(42°) = h2 / 16
By solving these two equations, we can find the values for h1 and h2, and thus the total height h of the television tower.