Final answer:
To find the distance of the hot air balloon from the landing field, we can use the Pythagorean theorem. By substituting the values into the formula, we find that the hot air balloon is approximately 1300.73 feet away from the landing field.
Step-by-step explanation:
To determine the distance of the hot air balloon from the landing field, we can use the Pythagorean theorem. The distance between the balloon and the landing field can be represented by the hypotenuse of a right triangle, with the height above the pond as one side and the distance from the pond to the landing field as the other side. Using the formula a^2 + b^2 = c^2, we can calculate the distance as follows:
c = √(a^2 + b^2)
where:
a = height above the pond = 500 feet
b = distance from the pond to the landing field = 1,200 feet
Substituting the given values into the formula, we get:
c = √(500^2 + 1200^2)
= √(250,000 + 1,440,000)
= √1,690,000
≈ 1300.73
Therefore, the hot air balloon is approximately 1300.73 feet away from the landing field.