Final answer:
Using trigonometry, specifically the cosine of a 30-degree angle, the ground distance traveled by a hot air balloon climbing to a height of 800 feet is calculated to be approximately 923.5 feet.
Step-by-step explanation:
The student's question relates to trigonometry, a branch of mathematics that deals with the relationships between the sides and angles of triangles. Given that a hot air balloon climbs at a 30-degree angle to reach a height of 800 feet, we can find the ground distance traveled using the cosine function of that angle, as we are dealing with the adjacent side in a right-angled triangle.
To find the ground distance (d) we use the formula:
d = height / cos(angle)
Plugging in the values we get:
d = 800 ft / cos(30 degrees)
Using a calculator:
d ≈ 800 ft / 0.866
d ≈ 923.5 ft