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Zolock
 one year ago
4. The diameter of circle C is 18 cm. Chord AD is the same length as a radius. Use this information, the diagram, and your experiences in geometry this semester to answer these questions. (Use pie = 3.14 .)
a.) What are the measures of angles BDA and DBA?
b.) What is the sine of angle DBA?
c.) Find the length of arc AB to the nearest hundredth.
d.) How does the length of arc AD compare to the length of arc AB?
e.) If EF = 1/2 BD, then what is the degree measure of arc EF?
Answer:
Zolock
 one year ago
4. The diameter of circle C is 18 cm. Chord AD is the same length as a radius. Use this information, the diagram, and your experiences in geometry this semester to answer these questions. (Use pie = 3.14 .) a.) What are the measures of angles BDA and DBA? b.) What is the sine of angle DBA? c.) Find the length of arc AB to the nearest hundredth. d.) How does the length of arc AD compare to the length of arc AB? e.) If EF = 1/2 BD, then what is the degree measure of arc EF? Answer:

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geerky42
 one year ago
Best ResponseYou've already chosen the best response.1dw:1433867445131:dw

geerky42
 one year ago
Best ResponseYou've already chosen the best response.1dw:1433867464274:dw So \(\triangle ACD\) is equilateral triangle, right?

geerky42
 one year ago
Best ResponseYou've already chosen the best response.1So can you tell me what \(m\angle BDA\) is?

geerky42
 one year ago
Best ResponseYou've already chosen the best response.1You do agree that \(\triangle ACD\) is equilateral triangle, right? So all angles in equilateral triangle are always ...?

geerky42
 one year ago
Best ResponseYou've already chosen the best response.1yeah. So since \(m\angle BDA\) is IN △ACD, what is angle?

geerky42
 one year ago
Best ResponseYou've already chosen the best response.1dw:1433867843613:dw

geerky42
 one year ago
Best ResponseYou've already chosen the best response.1Yeah, so there you go,

geerky42
 one year ago
Best ResponseYou've already chosen the best response.1dw:1433867910800:dw

geerky42
 one year ago
Best ResponseYou've already chosen the best response.1Yeah. BDA is 60. Now what is DBA?

geerky42
 one year ago
Best ResponseYou've already chosen the best response.1Correct. so you got answers for part A.

geerky42
 one year ago
Best ResponseYou've already chosen the best response.1Now for part B, you have \(\sin(30^\text o)\)

Zolock
 one year ago
Best ResponseYou've already chosen the best response.0so the sin for angle DBA is 30

geerky42
 one year ago
Best ResponseYou've already chosen the best response.1Not quite. \(\sin(30^\text o)\neq 30\)

geerky42
 one year ago
Best ResponseYou've already chosen the best response.1Do you have unit circle to check?

geerky42
 one year ago
Best ResponseYou've already chosen the best response.1Ok, you know 30 60 90 triangle? dw:1433868385520:dw So since \(\sin\theta\) is ratio of opposite side to hypotenuse side. In other words, \(\sin\theta = \dfrac{Opp}{Hyp}\), right?

geerky42
 one year ago
Best ResponseYou've already chosen the best response.1We have Opp = a and Hyp = 2a. What is Opp/Hyp?

geerky42
 one year ago
Best ResponseYou've already chosen the best response.1Not quite. Opp / Hyp = a / 2a So it's 1/2

geerky42
 one year ago
Best ResponseYou've already chosen the best response.1\(\sin(30^\text o) = \dfrac{Opp}{Hyp} = \dfrac{a}{2a} = \dfrac{1}{2}\) IS that clear?

Zolock
 one year ago
Best ResponseYou've already chosen the best response.0so sin(30 degrees) = 1/2

Zolock
 one year ago
Best ResponseYou've already chosen the best response.0nope I still need help with part C and part D I think I might me able to do part E on my own.

geerky42
 one year ago
Best ResponseYou've already chosen the best response.1Ok. Whole circle is \(360^\text o\), right?dw:1433869406908:dw Here, to find arc AB, we would need to find angle BCA. dw:1433869460152:dw

geerky42
 one year ago
Best ResponseYou've already chosen the best response.1Then we can find length of arc by using formula for circumference, kinda. \(Arc = \dfrac{m\angle BCA}{360^\text o} ~~2\pi r\)

geerky42
 one year ago
Best ResponseYou've already chosen the best response.1Here we have \(m\angle BCA = 120^\text o\)

geerky42
 one year ago
Best ResponseYou've already chosen the best response.1So arc length BA is \(\dfrac{120^\text o}{360^\text o}~~~2\pi r = \dfrac{2\pi r}{3}\) Make sense?

geerky42
 one year ago
Best ResponseYou've already chosen the best response.1You were given that diameter is 18. So clearly radius is 9.

Zolock
 one year ago
Best ResponseYou've already chosen the best response.0so the length of AB is 2πr/3

geerky42
 one year ago
Best ResponseYou've already chosen the best response.1Yeah. now plug in r = 9

Zolock
 one year ago
Best ResponseYou've already chosen the best response.0@geerky42 Can you finish helping me with part D and E when you get back online please I have to turn this in tomorrow.

geerky42
 one year ago
Best ResponseYou've already chosen the best response.1π^9? It's just \(\dfrac{2\pi 9}{3} = 2\pi3 = \boxed{6\pi}\)
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