Question

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°. Circle O is shown. Line segments L O , M O, and N O are radii. The length of L O is 6 centimeters. Angle M O N is 75 degrees. The measure of arc L M is 6.3 centimeters. Rounded to the nearest tenth of a centimeter, what is the length of arc LMN? 7.9 cm 10.2 cm 12.6 cm 14.2 cm

Answer 1

D

Explanation:

14.2

Answer 2

`LMN = 14.2`cm

Explanation:

Given

`r = OL = NO = MO = LO =6cm` -- radius

`LM = 6.3cm` -- arc

`\angle MON = 75^o`

(see attachment)

Required

The length of arc LMN

First, we calculate the length of arc MN using:

`MN = (\alpha)/(360) * 2\pi r` --- length of arc

In this case:

`\alpha = \angle MON = 75^o`

So, we have:

`MN = (75)/(360) * 2 * 3.14* 6`

`MN = (75* 2 * 3.14* 6)/(360)`

`MN = (2826)/(360)`

`MN = 7.85`

So, the length of arc LMN is:

`LMN = LM + MN`

`LMN = 6.3 + 7.85`

`LMN = 14.15`