Question

A hot air balloon hovers above its launch site at an altitude of 510 feet. The balloon operator sees a playground at a 10 degree angle of depression. Estimate the ground distance between the launch site and the playground to the nearest hundredth​

Answer 1

To estimate the ground distance, we use the angle of depression and the balloon's altitude, resulting in an estimated distance of approximately 2893.52 feet.

Step-by-step explanation:

To estimate the ground distance between the launch site and the playground, we need to use trigonometry. Given that the hot air balloon is at an altitude of 510 feet and the angle of depression to see the playground is 10 degrees, we use the tangent function which is the ratio between the opposite side (altitude) and the adjacent side (ground distance) in a right-angled triangle.

Setting up the equation:

1. Tan(10°) = Opposite / Adjacent
2. Tan(10°) = 510 feet / Ground Distance
3. Ground Distance = 510 feet / Tan(10°)
4. Ground Distance ≈ 510 feet / 0.1763
5. Ground Distance ≈ 2893.52 feet to the nearest hundredth

Thus, the estimated ground distance between the launch site and the playground is approximately 2893.52 feet.