Answer:
The length of arc LMN is 14.2cm
Step-by-step explanation:
First of all we have to calculate the circumference of the circle and then extract the portion that corresponds to MN
To solve this exercise we need to use the circumference formula of a circle:
c = circumference
r = radius = 6cm
π = 3.14
c = 2π * r
we replace the known values
c = 2 * 3.14 * 6cm
c = 37.68cm
As we know a circle is represented with 360 ° and they tell us that the angle of the MN part is 75 °, so we have to know the relationship with respect to the total
75° / 360° = 5/24
Now we multiply this number by the circumference and we will obtain the length of the arc MN
MN = 37.68cm * 5/24
MN = 7.85cm
Now we add the values of LM with NM and we will obtain the length of LMN
LMN = 6.3cm + 7.85cm
LMN = 14.15cm
round to the nearest tenth
LMN = 14.15cm = 14.2cm
The length of arc LMN is 14.2cm
