Calculating Arc Length: Radius, Central Angle, and Real-world Application

TLDR; Calculating arc length using radius and central angle, with real-world application to Earth's orbit.

🔍 Arc Length and Central Angle

Given a circle of radius 3 centimeters and a central angle of 120 degrees, we aim to find the length of the arc.

The formula for arc length is S = R x Theta, where S is the arc length, R is the radius, and Theta is the measure of the central angle in radians.

Converting 120 degrees to radians yields 2/PI divided by 3 radians, resulting in an arc length of approximately 6.28 centimeters.

🌍 Real-world Application

The Earth's orbit around the Sun is considered as a circle of radius 93 million miles, and since it takes one year for the Earth to travel around the Sun, the central angle for one month is 1/12 of 2/PI radians.

Using the formula S = R x Theta, with Theta as PI/6 and the radius as 93 million miles, the distance the Earth travels in one month is calculated to be approximately 48.7 million miles.