Question

Geometry, NEED HELP! WILL GIVE MEDAL!

Answer 1

okay so this one is in steps. first we should get the information we already know.
length BD is the same length as the diameter which is 18. AD is the same as the radius which is half of the diameter which equals 9.
so there is two of the three sides. to find the angle of DBA use the o/h function which is sine.

Answer 2

For some reason I don't think I learned what the o/h function is. That' or I just can't remember.

Answer 3

o/h=9/18=.5 do inverse sine .5 or archsine .5

Answer 4

thats fine your o/h is sine

Answer 5

Ok. so the sine is .5
What do I use the archsine for?

Answer 6

archsine you use to get the angle in degrees.

Answer 7

Oh! Woah. That' would've been helpful to know. So the archsine is .5?

Answer 8

no archsine OF .5 will get you your answer in degrees if you do this on a calculator it should look something like archsin(.5)= and then that number is your degrees

Answer 9

and yes it's helpful :)

Answer 10

did you get it?

Answer 11

pi/6

Answer 12

no it's the degree of <B or DBA

Answer 13

but pi/6 is equal to 30 degrees

Answer 14

But I already know that Angle B is 30 degrees because the triangle is a right triangle and therefore follows the 30-60-90 triangle thing

Answer 15

well in that case you should now a. and b.

Answer 16

know*

Answer 17

Yes, I guess I should've been more specific. I need help with C, D, and E

Answer 18

haha okay that's fine I can still help. I can show you and very easy way to get length AB

Answer 19

ok

Answer 20

If I find AB then I can do question D on my own. Then I'll just need help with E

Answer 21

however your not suppose to know this until calculus so...shhh haha

rename length AD to A
rename length AB to B
and rename length BD to C

to find B use this formula

b/sin b=c/sin c
this is easy because it's a right triangle.
sin of c or sin of 90 =1
sin of b is sin of 60=0.866
now it will look like
b/.866=18/1
simplify
b/.866=18
multiple both sides by .866
b= 18 x .866
b=15.588

Answer 22

so... the length of AB is 15.5?

Answer 23

that is correct

Answer 24

are you ready for the last one?

Answer 25

The length of the arc?

Answer 26

Also for D then. The relationship is about...

Answer 27

1.7 * length-arc AD = length-arc AB

Answer 28

@Master_General_B_C

Answer 29

sorry I grab something to eat

Answer 30

That's ok.

Answer 31

okay so which do you need help with?

Answer 32

So for D the relationship is about 1.7 * length-arc AD = length-arc AB?

Answer 33

yes it should be

Answer 34

Ok. Now for E

Answer 35

okay

Answer 36

now do you have an arch formula?

Answer 37

No. I would probably have to look in my textbook

Answer 38

hmm...I have one, but it's a calculus one and it might confuse you.

Answer 39

They always say you need the central angle measure but we don't have a central angle.

Answer 40

we can get one :)

Answer 41

make a straight line from E to C and F to C

Answer 42

this will be an equilateral triangle. because they all are the radius length (9)

Answer 43

That would make it about a 45 degree angle right? but how do we know the exact measurement?

Answer 44

the formula is (60/360) x 2pi r
and it would be 60 because 60 x 3 = 180

Answer 45

this will give you an answer of 9.42

Answer 46

so. The length of the arc is 9.42?
Then what's the measure?

Answer 47

So can you tell me more specifically why it's 60?

Answer 48

60 would be the answer

Answer 49

How is 60 the answer? and what is the 9.42 for then?

Answer 50

sorry I went too far that formula is to find the length you were only looking for the degree. so that formula is nothing to you...yet

Answer 51

so the length is 9.42

Answer 52

yes but you are looking for the degree which is 60

Answer 53

So how does the degree become 60 from 9.42?

Answer 54

forget about the 9.42 that is the length I went too far. go back to when we made the lines from E and F to C. the angle of ECF will be the same angle of the arch of EF

Answer 55

Yes.

Answer 56

so do you get it now?

Answer 57

Not really. How do I know that the angle of ECF is 60 degrees?

Answer 58

okay. if you take a point from the side of a circle to the center that would be the radius. we know the radius is 9 so EC, EF, and FC are all 9. do you get that?

Answer 59

Ok.

Answer 60

so how does that relate to the 60 degrees of the arc?

Answer 61

Sorry, i'm probably making this really hard for you.

Answer 62

because the angles will all be the same. <C, <E, and <F will all be the same angle in degrees (60) the arc length IN DEGREES will be the same as the angle that faces it, in this case <C

Answer 63

oh. ok got it. thanks

Answer 64

you are welcome.