The diameter of a circle is 8 centimeters. A central angle of the circle of the circle intercepts an arc of 12 centimeters. What is the radian measure of the angle?

Question

contestada

Respuesta :

calculista calculista · Answer 1 · 2019-01-06T23:02:27+01:00

Answer:

The measure of the angle is [tex]3\ radians[/tex]

Step-by-step explanation:

we know that

The formula to calculate the arc length of a circle is equal to

[tex]L=r\theta[/tex]

where

r is the radius of the circle

[tex]\theta[/tex] is the measure of the angle in radians

In this problem we have

[tex]L=12\ cm, r=8/2=4\ cm[/tex]

substitute in the formula and solve for [tex]\theta[/tex]

[tex]12=4\theta[/tex]

[tex]\theta=12/4[/tex]

[tex]\theta=3\ radians[/tex]

MrRoyal MrRoyal · Answer 2 · 2022-02-07T13:36:04+01:00

The radian measure of the angle is 3

The length of an arc is calculated as:

[tex]l = \frac d2* \theta[/tex]

Where

l represents the length of the arc

d represents the diameter

[tex]\theta[/tex] represents the radian measure of the angle

So, we have:

[tex]12 = \frac 82* \theta[/tex]

Divide 8 by 2

[tex]12 = 4* \theta[/tex]

Divide both sides by 4

[tex]\theta = 3[/tex]

Hence, the radian measure of the angle is 3