Question

Find The Circumference. If Arc Length Is 19.68 and the central angle is 94.

Answer 1

Here's The Picture

Answer 2

\(s = \dfrac{\theta}{360^o}2 \pi r\)

s = arc length
\(\theta\) = central angle measure in degrees
r = radius of circle

Answer 3

You are given arc length and central angle.
Solve the equation for \(2 \pi r\) and plug in the known values.

Answer 4

what's the radius @IMStuck

Answer 5

@IMStuck

Answer 6

You don't need the radius.
\(2 \pi r\) is the circumference.
Take the formula above, and solve it so you have \(2 \pi r\) only on the right side.
That means divide both sides by theta/360, which means multiply both sides by 360/theta.

\(\dfrac{360^o} {\theta} \times s = \dfrac{360^o} {\theta} \times\dfrac{\theta}{360^o}2 \pi r\)

\(\dfrac{360^o} {\theta} \times s = 2 \pi r\)

\(\dfrac{360^o s} {\theta} = 2 \pi r\)

You see the last line above. The right side is 2*pi*r which is the circumference.
All you need to do is insert the arc length and angle on the left side and you'll get the circumference.

Answer 7

THANK YOU!!! @mathstudent55

Answer 8

You're welcome.

Answer 9

ok next question.... I'll just post it