Answer:
[tex]LMN = 14.2[/tex]cm
Step-by-step explanation:
Given
[tex]r = OL = NO = MO = LO =6cm[/tex] -- radius
[tex]LM = 6.3cm[/tex] -- arc
[tex]\angle MON = 75^o[/tex]
(see attachment)
Required
The length of arc LMN
First, we calculate the length of arc MN using:
[tex]MN = \frac{\alpha}{360} * 2\pi r[/tex] --- length of arc
In this case:
[tex]\alpha = \angle MON = 75^o[/tex]
So, we have:
[tex]MN = \frac{75}{360} * 2 * 3.14* 6[/tex]
[tex]MN = \frac{75* 2 * 3.14* 6}{360}[/tex]
[tex]MN = \frac{2826}{360}[/tex]
[tex]MN = 7.85[/tex]
So, the length of arc LMN is:
[tex]LMN = LM + MN[/tex]
[tex]LMN = 6.3 + 7.85[/tex]
[tex]LMN = 14.15[/tex]
