Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an

step 1 In this question, given, radius of the circle r equal to 100 semi, and an arc of length, L equal

Find the degree measure of the angle subtended at the centre...

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Key Concepts

Central Angle in Radians

The central angle is the angle formed at the center of a circle by two radii that extend to the endpoints of an arc. When measured in radians, this angle directly relates to the arc length by the formula s = r?. Understanding radians is essential in many areas of mathematics, especially in trigonometry and calculus, because it provides a natural way to describe angular measurements in terms of the circle's radius.

Radian to Degree Conversion

Radian to degree conversion is the process of converting an angle measurement from radians, where the full circle is 2? radians, to degrees, where the full circle is 360 degrees. This conversion is done using the formula: degrees = (180/?) × radians. Mastery of this conversion is important in numerous areas of mathematics, physics, and engineering, where different units of angle measurement may be used.

Arc Length

Arc length refers to the distance along the curved line making up a portion of a circle's circumference. In the context of circle geometry, it is directly related to the central angle subtending the arc. The formula s = r?, where s is the arc length, r is the radius, and ? is the angle in radians, establishes this relationship and is fundamental to solving problems related to arcs and sectors.

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