Answer :
The measure of the arc that represents the part of Earth you can see from a hot air balloon at an altitude of 1.2 miles is 2.8°. To find this, first calculate the distance to the horizon using the formula [tex]\sqrt{2rh}[/tex]. Then, find the visible arc measure based on the Earth's circumference, resulting in an arc measure of approximately 2.8°.
To determine the measure of the arc that represents the part of the Earth you can see from a hot air balloon at an altitude of 1.2 miles, we will use the formula for distance to the horizon:
- [tex]\text{Distance to the horizon}= \sqrt{2rh}[/tex]
Where r is the radius of Earth (4000 miles), and h is the observer's height above the Earth's surface (1.2 miles).
Calculate the distance to the horizon:
- [tex]\sqrt{2 \times 4000 \text{ miles} \times 1.2 \text{ miles} }= \sqrt{9600} = 97.98 \text{ miles (approximately 98 miles)}[/tex]
Calculate the arc measure:
- [tex]\text{The circumference of the Earth} =2\pi r = 2 \times \pi \times 4000 \approx 25132.74 \text{ miles}[/tex]
The fraction of the circumference visible =[tex]\frac{(2 \times \text{Distance to the horizon})}{\text{Circumference}}[/tex]
- [tex]\text{Visible arc measure}= \frac{2 \times 98}{25132.74} \times 360^\circ \approx 2.8^\circ[/tex]
Thus, the measure of the arc that represents the part of the Earth you can see from the hot air balloon is approximately 2.8°.
Question: You are flying in a hot air balloon about 1.2 miles above the ground. Find the measure of the arc that represents the part of Earth you can see. Round your answer to the nearest tenth. (The radius of Earth is about 4000 miles)
The arc degree representing the portion of Soil you'll see from the hot air balloon is around 0.0 degrees.
How to Solve the Arc Degree?
To discover the degree of the arc that represents the portion of Earth you'll be able to see from the hot air balloon, you'll be able utilize the concept of trigonometry.
To begin with, we got to discover the point shaped at the center of the Soil by drawing lines from the center of the Soil to the two endpoints of the circular segment. This point will be the central point of the bend.
The tallness of the hot discuss swell over the ground shapes a right triangle with the span of the Soil as the hypotenuse and the vertical separate from the center of the Soil to the beat of the hot discuss swell as the inverse side. The radius of the Soil is around 4000 miles, and the stature of the swell is 1.2 miles.
Utilizing trigonometry, able to calculate the point θ (in radians) utilizing the equation:
θ = arcsin(opposite / hypotenuse)
θ = arcsin(1.2 / 4000)
θ ≈ 0.000286478 radians
To discover the degree of the circular segment in degrees, we will change over the point from radians to degrees:
Arc measure (in degrees) = θ * (180 / π)
Arc measure ≈ 0.000286478 * (180 / π)
Arc measure ≈ 0.0164 degrees
Adjusted to the closest tenth, the arc degree representing the portion of Soil you'll see from the hot air balloon is around 0.0 degrees.
Learn more about arc degree here: https://brainly.com/question/15815055
#SPJ1
