Let us consider a circle with radius r

Length of Arc Formula.jpg

 

Arc is a portion of the circle.

 

Let the arc subtend angle θ at the center

Then,

Angle at center = Length of Arc/ Radius of circle

θ = l/r

 

Note: Here angle is in radians.

Let’s take some examples

If radius of circle is 5 cm, and length of arc is 12 cm. Find angle subtended by arc

Length of Arc Formula 2.jpg

View Answer

 

If angle subtended by arc is 1 radian, and radius of circle is 1 cm. Find length of arc

Length of Arc Formula 3.jpg

View Answer

 

If angle subtended by arc is π radian, and length of the arc is 2 π cm. What is the radius of circle?

Length of Arc Formula 4.jpg

View Answer
  1. Chapter 3 Class 11 Trigonometric Functions
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Transcript

Let us consider a circle with radius r Arc is a portion of the circle. Let the arc subtend angle θ at the center Then, Angle at center = Length of Arc/ Radius of circle θ = l/r Note: Here angle is in radians. Let’s take some examples If radius of circle is 5 cm, and length of arc is 12 cm. Find angle subtended by arc Given radius = r = 5 cm Length of arc = l = 12 cm We know that   θ = l/r   θ = 12/5 ∴ Angle subtended by angle arc = 12/5 radians If angle subtended by arc is 1 radian, and radius of circle is 1 cm. Find length of arc Given radius = r = 1 cm Angle = θ = 1 radian We know that   θ = l/r   1 = l/1   1 = l   l = 1 cm ∴ Length of the arc = 1 cm If angle subtended by arc is π radian, and length of the arc is 2π cm. What is the radius of circle? Given Length of arc = l = 2π cm Angle = θ = π radian We know that   θ = l/r    π = 2π/r   r = 2π/π   r = 2 cm ∴ Radius of circle = 2 cm

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.