# The Lesson Of Finding The Arc Length Of A Circle

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I choose a word problems, which is part of the lesson of finding the arc length of a circle. To address this concept, I want to assign the following word problem to the students:

“A satellite orbiting the earth in a circular path stays at a constant altitude of 100 kilometers throughout its orbit. Given that the radius of the earth is 6370 kilometers, find the approximate distance that the satellite travels in completing 70% of one complete orbit.”

The standard that is covering here is CCSS.MATH.CONTENT.HSG.C.B.5 (Common Core State Standards Initiative, n.d.), which is “Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. For this lesson, the students need to know how to use the formula to find the circumference of a circle, but also, how the find the measurement of an arc, without forgetting that they need to find only when the satellite completes 70% of the orbit, and how many degrees are 70% of the arc. Students should have a background on how to change the percent to a decimal, or to a fraction. Also, there are multiple ways on how the students can find the answer. It is probably that most students will only use the radius of the Earth, which is 6370 km. However, they can miss important information: the satellite is orbiting 100 km above the Earth’s surface. They need to add