Final answer:
Using trigonometry, the height of the tower can be calculated as approximately 2663 feet using the tangent of the angle of elevation (26.8º) at a distance of one mile (5280 feet) from the tower. The provided options do not include this result, indicating a potential issue with the question or the answer choices.
Step-by-step explanation:
To approximate the height of the television transmitting tower, we can use trigonometry, specifically the tangent function, because we have the angle of elevation and the distance from the observer to the base of the tower. The tangent of an angle in a right triangle is the ratio of the opposite side (the height of the tower, in this case) to the adjacent side (the distance from the observer to the base).
The formula for the tangent of the angle of elevation (26.8º) is:
tan(26.8º) = height of the tower / 5280 feet
Using a calculator, we find that tan(26.8º) is approximately 0.5045. We can then solve for the height of the tower:
0.5045 = height / 5280 feet
height = 0.5045 * 5280 feet
height ≈ 2662.76 feet
So, the approximate height of the tower to the nearest foot is 2663 feet, which is not one of the options provided in the question. Therefore, there might be a mistake in the question or the options given. We need to check the question parameters again or consult additional sources for the correct answer options.