# Angles and Arcs

• Jul 13th 2009, 06:54 AM
ineedhelp1
Angles and Arcs
the diamater of CIRCLE D is 18 units long find the length of each arc for the given angle measure

http://i25.tinypic.com/t6ee5c.png

(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
• Jul 13th 2009, 07:11 AM
Plato
About halfway down is the formula for arc length.
Be careful, you must change degrees to radians.
• Jul 13th 2009, 07:34 AM
ineedhelp1
i still dont get it to be hon est
• Jul 13th 2009, 07:51 AM
Plato
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 $(9)\left(\frac{100\pi}{180}\right)$.
• Jul 13th 2009, 08:22 AM
ineedhelp1
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??
• Jul 13th 2009, 08:30 AM
Plato
It must be $m(\angle DC{\color{red}E}) = 100^o$.
If so that is the correct answer.
• Jul 13th 2009, 08:34 AM
ineedhelp1
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
• Jul 14th 2009, 07:56 AM
ineedhelp1
sorry for double post but i gotta turn this in today and i was wondering if i got the answers right
• Jul 15th 2009, 04:50 AM
HallsofIvy
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".