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You fly a hot air balloon 1.5 miles above the ground. What is the measure of \( \overarc{BD} \), the portion of Earth that you can see? Round your answer to the nearest tenth. (Earth's radius is approximately 4000 miles.)

Answer :

Final answer:

To find the measure of BD⌓, the visible portion of Earth's surface from a hot air balloon 1.5 miles above the ground, convert the height to kilometers and use the formula D = 112.88 km × √h to get the distance to the horizon, which is about 175.4 km. Then, calculate the semicircular distance visible by using C/2 = (π × D) / 2, which results in approximately 276.1 km for the measure of BD⌓.

Explanation:

To calculate the measure of BD⌓, the portion of Earth's surface that is visible from a hot air balloon 1.5 miles above the ground, you can use the formula for the distance to the horizon, given as D = 112.88 km × √h, where h is the height above the Earth's surface. In this case, we must convert the height of 1.5 miles to kilometers before applying the formula, as the formula uses kilometers.

The conversion from miles to kilometers is 1 mile = 1.60934 kilometers, so 1.5 miles is approximately 2.414 km.

Inserting h = 2.414 km into the formula, we get:

D = 112.88 km × √2.414

D = 112.88 km × 1.5535 (approx)

D ≈ 175.4 km (rounded to the nearest tenth)

This is the straight-line distance to the horizon. To find the measure of the arc BD, which is the portion of the Earth's surface visible, we can treat this distance as the radius of a circle and calculate the circumference. However, since we are only looking at the visible part, which is a semicircle, we use half of the circumference C = π × D.

The measure of BD⌓ is therefore approximately:

C/2 = (π × 175.4 km) / 2

C/2 ≈ 276.1 km

Thus, the measure of BD⌓ to the nearest tenth is 276.1 km.

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Rewritten by : Barada

Answer:

3.1

Step-by-step explanation:

If you are doing this for big ideas, the answer ended up being 3.1

I'm sorry if you wanted the work, I found the answer from something else that didn't show the work but this was the correct answer...