Angles and Arcs

**ineedhelp1** · July 13th 2009, 06:54 AM

the diamater of CIRCLE D is 18 units long find the length of each arc for the given angle measure

(ARC)LM if m<LDM=100

- (ARC)MN if m<MDN = 80

- (ARC)KL IF m<KDL=60

- (ARC)NJK if m<NDK=120

- (ARC)KLM if <KDM=160

- (ARC)JK if m<JDK = 50

Please solve this for me so i can do the 5 other that i have

**Plato** · July 13th 2009, 07:11 AM

Read this.
About halfway down is the formula for arc length.
Be careful, you must change degrees to radians.

**ineedhelp1** · July 13th 2009, 07:34 AM

i still dont get it to be hon est

**Plato** · July 13th 2009, 07:51 AM

The length of an arc is $\ell = \phi r$ where $\phi$ is the central angle and $r$ is the radius.
Now $\phi$ is in radians so you must change to degrees.

In your question the arc $ML$ is subtended by an angle of $100^o$ and radius of the circle is $r=9$ .

Thus the length of the arc $ML$ is $(9)\left(\frac{100\pi}{180}\right)$ .

**ineedhelp1** · July 13th 2009, 08:22 AM

ok looks my teacher did this problem

the diameter of CIRCLE C is 32 units long find the length of each arc for the given angle measure

(ARC)DE if m<DCF=100

she got the anwser 27.93 is she right??

**Plato** · July 13th 2009, 08:30 AM

It must be $m(\angle DC{\color{red}E}) = 100^o$ .
If so that is the correct answer.

**ineedhelp1** · July 13th 2009, 08:34 AM

yeah it is my bad i try to i tried to follow what she did but i get a different answer from what you posted on the problem

i got 15.70 units

btw my teacher she got the diameter and mulitplied by pie so that what i did and got that answer..

here my answers for all the q;s

-ARC)LM if m<LDM=100

- (ARC)MN if m<MDN = 80

- (ARC)KL IF m<KDL=60

- (ARC)NJK if m<NDK=120

- (ARC)KLM if <KDM=160

- (ARC)JK if m<JDK = 50

- 15.70
- 12.56
- 9.42
- 37.69
- 31.41
- 7.85

i forgot

100/360 = L/18 then i multiply 18 * 3.14 then 100/360 = L/56.54 cross multiply then 5654/360 = 15.70

**ineedhelp1** · July 14th 2009, 07:56 AM

sorry for double post but i gotta turn this in today and i was wondering if i got the answers right

**HallsofIvy** · July 15th 2009, 04:50 AM

Anothe way of looking at it. A circle of diameter 18 has circumference $18\pi$ and, of course, is an "angle" of measure 360 degrees. The ratio of those is $\frac{18\pi}{360}= \frac{\pi}{20}$ .

A an angle $\theta$ degrees will cut off an arc of length L in that same ratio:
$\frac{L}{\theta}= \frac{\pi}{20}$ so

$L= \frac{\pi\theta}{20}$ .

Your first, second, third, and sixth are correct. Your fourth and fifth answers are wrong! I don't know how you did that!

Note that, for the third one, the angle is 60 and you got, correctly, 9.42. The fourth has angle 120, exactly twice the angle in three so the arclength should be 2 times 9.42, which is NOT "37.69" which is 4 times as large.

Similarly, the angle for the fourth one is 160 degrees, exactly twice the 80 degrees in number 2. The arclength should be 2 times the 12.56 you got for that, not "31.41".

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