Final answer:
Using the tangent of the angle of depression and the altitude of the balloon, the calculated distance to the house is 1364.4 feet, but the closest provided choice is 1236.6 feet.
Step-by-step explanation:
To find the distance from the pilot to the house in a hot air balloon at an altitude of 2926 feet with an angle of depression of 25°, we use trigonometric relationships. Specifically, the tangent of the angle of depression will equal the opposite side (the distance from the pilot to the house directly below, which we are trying to find) divided by the adjacent side (the altitude).
The tangent of 25° is equal to the opposite/adjacent, which gives us the equation tan(25°) = distance/2926 feet. We solve for distance by multiplying both sides by 2926 feet:
distance = 2926 feet × tan(25°)
Using a calculator:
distance = 2926 × 0.4663 (tan(25°) approximately)
distance = 1364.4 feet
This result is not exactly one of the provided choices, which suggests there might be a typo in the question or the answer choices. However, the provided answer closest to our calculation is:
The house is 1236.6 feet from the pilot.