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9 December, 11:28

01:29:

In circle o, the length of radius OL is 6 cm and the length of

arc LM is 6.3 cm. The measure of angle MON is 75°.

Rounded to the nearest tenth of a centimeter, what is the

length of arc LMN?

6.3 cm

6 cm

7.9 cm

10.2 cm

12.6 cm

14.2 cm

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Answers (1)
  1. 9 December, 11:58
    0
    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
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