Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 year ago

# Determine the length of the arc of a circle with radius 15 m and a central angle of 100°??

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a formula is given in Trig for arc length, but the central angle must be in radians

... instead you can use a proportion

Angle A / arc length a = angle B / arc length b

use 360, an entire circle for angle B .. and use the circumference of the circle as arc b

100 / a = 360 / (2pi*15) <<<< solve for a

a = (100/360)* (2pi*15) = 26.18 m

• --

L = (100/360) x 2π x 15 m

L = (10/36) x 30π. m

L = (5/18) x 30π m

L = (5/6) x 10π. m

L = (25/3) π m

L = 26•2 m

• The circumference of a circle is the arc length subtending a central angle of 360°. It follows that the arc length subtending a central angle of 100° would be 100°/360° or 5/18 of the circumference. So, for a radius of 15m and a central angle of 100°, the arc length A would be:

A = (100°/360°) C

A = (100°/360°)(2 π r)

A = (100°/360°)(2* π *15)

A = (5/18)(30 * π )

A = 150π/18

A = 25π/3

A = (25/3)(22/7)