Question

In the diagram below, Θ is measured in radians. Which equation represents the relationship between the radius, r, and arc length, s?

Circle O is shown. Line segments A O and B O are radii with length r. Angle A O B has a measure of theta. Arc A B has a measure of s.

Answer 1

Answer:

$s = r \theta$

Step-by-step explanation:

There is a relationship between the central angle of a sector and the length of the arc enclosed by the two radii of the sector.

When the central angle of the sector

$\theta$

is measured in radian.

Then the relation between this angle and and the radius r, and the arc length , s is

$s = r \theta$

Answer 2

The equation that represents the relationship between the radius r, theta arc length s is: $s = \theta \times r$

Given information:

• Circle O is there.
• AO and BO are line segments being radius of given circle.
• The arc AB has length = s units

How can we use a full rotation?

Whole circumference is covered by 360 degrees rotation.

How  to find the relation between angle subtended by the arc, the radius and the arc length?

$2 \pi ^c = 360^{\circ} = \text{full circle's circumference}$

Thus, from above we have:

$1 ^c \: \rm covers \: \dfrac{circumference}{2\pi}\\\\or\\\theta^c \: \rm covers \: \dfrac{2\pi r \times \theta} {2 \pi}\\\\\theta^c \: \rm covers \: \: \theta \times \text{r unit length of arc}$

Since arc given is of s length, thus we have:

$s = \theta \times r$

Thus, the equation that represents the relationship between the radius r, theta arc length s is: $s = \theta \times r$

Learn more about arc length here:

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