#geometry-and-trigonometry
1 messages ยท Page 332 of 1
If I draw a square and put the diagonal between the center of each circle, then the radius is not applicable, right? I'm still not sure how this will work
<@&268886789983436800> help please
ok one sec
Need help w this
ah I see
This channel is doing real well
The length of the hypot is R+r
I rly need help on that one
ok what have you tried
Euler, how do I account for the small space at the bottom?
@tender prawn so /
chicken602, do you know what I should do?
uh lemme take a look
a not so elegant way would be using geometric sequence
hold on
Im so confused
bruh at least think about it before asking
shaded region over whole region?
Shaded
area of shaded region isn't 9 pi btw
Oh
area of shaded is whole circle - white circle (4pi)
try 2((R-r)^2) = (R+r)^2
is big R for the big circle or small?
R for big, r for small
oh im dumb lol
what's the total region
like u have shaded/total
what's the total
u know shaded is 5pi
mhm
So 9-4=5
5/9 should be the correct answer
label the sides and do some pythagorean theorem
Can u help me
im not gonna tell u the answer
No but help me
label the sides you currently have
and what tool do you have relating to right triangles
Idk
write down the side lengths you currently have on the diagram
mhm
so using the pythagorean theorem
which length can you find next?
currently there are two unknown side lengths
AC and AD
mhm
So
what is c
2+rad(1)=c
wat
C is 2
no u have 4 + 1 = (AC)^2
Oh
so what can u do now
Sq root
should be
Ok
Im not good with traiangles
I mena
Not like that
I just didnt understand
Im preping for the shsat
if u ask DA line yes it is 3
Whats da
idk how proper of a solution u need but u can like
What
can anyone 104.I
Is fhat
look at the case where it's a square because it deosn't specify what parallelogram it is
help*
Make fullscreeb pls
okay i will try
Looks tough
You should hide that part lol
Lol
Its his prof
Maybe?
Im not tryna be stalky
I am just curios
kekw
maybe nick lord is his prof
actually as i said it is not my question and i just help my friend at this question
there is not anything illegal ๐
its just for your own safety
Those problems are hard holy
i was trying for 2hours
i am a bit confused i think maybe there is some easy way i dont know
Anyway the ratio between areas most certainly is invariant so just let the parallelogram be a square
^
can we call all parallelogram square?
no
its just asking for a solution
it doesn't specify what type of parallelogram so you can solve it for the case where it's a square and get the answer
The intended method involves sum and difference of triangles whose areas are fractions of the parallelogram's
What is your goal?
and the second line
im supposed to prove the second line
ok elmme send the problem
You know you can do it with a single picture
like on a unit circle
Yeah, consider a triangle with those angles
It has to have those angles
not in particular no
R^2[sin(2a)+sin(2b)+sin(2c)]
1/2 ab sinC and 2R^2 sinA sinB sinC?
ok
Look at the three centre triangles
Area (1/2)R^2sin(2a)
Or you can do the whole triangle in one go using the extended sine rule
(1/2)xysin(a) where x=2Rsin(b) and y=2Rsin(c)
So if you equate you get the formula
There is always an easy way to do things
Think smart not hard
ahh okay
yep
kk
is this a olympics question?
hm?
you do not need to understand anything. it is writing values โโcd cember
there is half circle
you can understand br: cm
<@&286206848099549185>
ive seen this question 99^10x9999 times in the past 2 days
what does this mean
congruent
thats a weird ass question
Think this is a trig question. How do I solve for x in
I've tried everything I know of, so I am restorting to here
x in what
yeah
whats the question
oh
solve for x
oh
multiply by two and take sqrt of both sides probably
I would do that, but that doesn't give me the answer I'm looking for.
Which channel would I post this in
just plug in values?
or u can do the whole shift thing
its probably d
$x(36+x)=60^2$
AV8312
By the power of a point theorem
what's the actual question
i see a statement,
two triangles with markings and a blue pip
what's there to solve?
how do I do this
the justification for congruence if it exists
yes
so for #2 it would be none?
yes
Hi, how can I know the direction of the following normalised vector? [0.7 -0.7]
Wait t/c?
how would i do this question?
know properties of the sine function and/or unit circle
how would i start the question
if you're familiar with the unit circle you'd know that sin(x) = 0 when x is a multiple of 180. Find all multiples of 180 that are less or equal to* than 720 degrees*
hey
i have a math question
In parallelogram QRST if TU=18 find TR.
can someone pls help
<@&286206848099549185>
anyone pls
ok so if TU = 18, then that must mean that RU also equals 18, yes?
yeah
๐
how would i start this question?
,rotate
@thorny lintel do you know in which quadrants tan(x) is negative?
@upper karma quadrant IV and II
right, and are you allowed to use a calculator to solve this problem?
yes
okay, so you'd do arctan(-1.428) and you should get about -55* for that
so -55 would be the only value?
no
remember that you need all values within the domain of [90, 270]
and for tan to be negative, it needs to be in the second and fourth quadrants. So you need to find the reference angles in quadrants II and IV
oh so -55 is just an angle
yes, put you can't use -55 because it's not in the domain [90, 270]
Do you know how to find the reference angle?
i have some knowledge of it but not in depth
can you find the reference angle of 55 in the second quadrant?
would it just be 55?
no
oh iโm not sure then
so the value of the angle MUST be in quadrant 2 or quadrant 3. because
Quad 1: 0-90
Quad 2: 90-180
Quad 3: 180-270
Quad 4: 270-360
and your sheet says to find an angle between 90 and 270. Do you now understand why 55 wouldn't work?
yes
after you guys are done can i get a bit of help
Anyone know how I would solve this tan6= 30000/x
@upper karma wait so how would arctan help?
since tan is positive in quadrant 3, that restricts the value of the angle to quadrant 2 (where tan is negative). To find the reference angle in quadrant 2, we just do 180 - 55 = 125. We can check our work by doing tan(125) and seeing that our answer is indeed -1.42 @thorny lintel
How did you write that in the calculator
Yeah thatโs actually right thx
arctan will give us the angle
the value of x
The diagonals are perpendicular.
The diagonals bisect each other.
One diagonal bisects the opposite angles.
One pair of opposite angles are congruent.
pls help
ooh ok thank you @upper karma
np
;-;
we know that they bisect each other, right?
of course they do, we can see it. so that leaves only 3 other answers
we also know that the diagonals are perpendicular
yeah
so is it b?
its not a c or d
holup
how is b crossed out
ac bisecs db?
wait
probably
eni meeni mini moe catch a tiger by its toe if it hollers let it go eeni meeni minne moe
oh lol
I mean this one: The diagonals bisect each other.
oh ok
thats what i thought lol
wait
are the diagnols perpendicular in rectangles
no right
Remember that a square is a rectangle, so all rectangles except squares do not have perpendicular diagonals.
lmaqoo
just do this then multiply by conjugate then back to trig form
Yo
For number 42
Would it be
16 or 24
Since
AY is 8
Y to z
Should be 16 or 24
help my friend needs help and idk how to do it
hey can someone help me with this geometry word problem?
Daniel installed his own 38- foot fladpole. He added a wire with one end attached to the top of the pole and the other end attached to the ground 12 feet from the base of the pole. How long was this wire?
@here
maybe proving AB is parallel to DC and perpendicular to AD and BC (so quadrilateral becomes a rectangle), then pythagoras to show AB = BC (from a rectangle to square)
I got y=x-1 for the first but the rest I am confused
this is not enough, you will end up with a rhombus
yeah im saying do that for every side
ohhhhhhhhhhhhhhhhhhhhhhh
ahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
still not enough
ahhhhhhhhhhhhhhhhhhhhhhhh
Iโm very confused about this but it could also be y=x-2. I just need help with these three
so for the first one
if its being enlarged by a scale factor of 1/3
y = x - 3
enlarged by 1/3
what do u think we have to do
@upper karma
Instead, check every angle is 90ยฐ
alr
its says centred at the originx
how do we factor that into our calcs if we dont know the original position of the shape
Bro can you tell me how to do it. If you canโt itโs fine Iโm just confused and need someone to help.
@upper karma
Or wait, my suggestion is stupid. Every side has the same length, and opposite sides are parallel is easier
these questions are quite odd
or i might be doing them wrong
to englarge them i did multiply them
but then
Thatโs what I got for the first one mate
yeah
Itโs one question but the rest is what you apply for each graph
wait hold on
wdym?
yeah I got an error on that
thanks
Like y=x-3 is the equation that is dilated by and is used for questions 1,2,3
yes
So Iโm confused on what to do in 2 and 3 since the equation y=x-3 had multiple coordination
Coordinates*
a coordinate is one point
a line has many points
they are saying that u need to enlarge the whole line by that scale factor
So question 2. Has a scale factor of 2 and centered at the origin
Man anyone? This is due in 15 mins
Itโs okay if you canโt just say it Iโll just do what I can
just multiply by 2
like u did at with number 1
but they said the scale factor is 1/3
I didnโt multiply for the first I cut it down by 1/3 since itโs dilated
cut it down
dilated basically mean to enlarge
the scale factor is 1/3
so u multiplied the equation of the line (x - 3) by 1/3
so for the second one
just multiply it by 2
have u guys not studied enlargements
What? So multiply (x-3)*2 and no just got these three pwctice wiestikns today
Practice questions*
yes multiply it by 2
Got 2x-6..........
Tf idk you probably know this better than me
yeah 2x-6 is the answer
i was just asking bc i thought u also had the answers
do u understand why we multiplied by 2
its the same as Q1
u multiplied by 1/3
bc that was the scale factor
does that make sense?
Yeah scale factor is dilated so for 3 it would be the centered coordinate and scale factor also multiplied by 2?
But (-1,-2) is the center now but it would still be the same the same again?
Due in 5 mins now. Iโll try dis Man. Thanks for trying to help me
Yeah to (1,-2) for question 3
yeah
So the same step?
yeah
if they havent toild u to draw the graph, then the centre does not matter much
Which is literally the same equation.
yeah
Itโs y=2x-2 again?
they are throwing extra info at u to confuse u
nope
y = 2(x - 3)
cant br y = 2x - 2
Alright Iโll just ask my teacher about this tomorrow. Like we didnโt even start of by learning just practicing
aight
But thanks mate
yw
Alright itโs correct. But how you get y=2(x-3) when you said itโs the same equation if the center is Changed?
lemme send a vid in a bit
srry channelk takenb
What video you sending?
Same as before @upper karma
Make sure the sides are equal length, and opposite sides are parallel
nvm about the video
but u dont need to care about the origin
if it says enlarge
and they've given u an equation
ur probably gonna study enlargements soon
and it will all make sense
what is the formula for area of circle?
@oak citrus literally same thing asked in #prealg-and-algebra
clown to clown
use pythagoras and solve
Opps forgot to add the ^2
@main meadow can you point out what the hypotenuse of that triangle is?
Longest sode
what is the longest side in this case?
5a
and if c in this equation is the hypotenuse, would you agree that whatever a and b are they equals a^2+b^2=5a^2
Teah
3a for a abd 12 for b
ok so with this knowledge can you setup the equation again?
Yeah
ok do that and send
@oak citrus is a man of patience, commitment and s h e e r f o c k i n g w i l l
Oh is 9
?
A=9
did you finish problem
Yes
i havent done the problem but send work
6Rad2
No it's wrong
send pic of your work
what's rad doing in this?
Mb

yes
Oops i forgot to rad
rad as in sqrt?
I'd suggest you call it square root instead of radical
depends on what quadrant you need
tanx < 0 will always give an angle in quad 4
if the angle is in quad 2, you add pi / 180
ok thank you
pick a postulate and then apply it
well i only know the congruence of one angle
and one side
so i cant prove anything
@zenith garnet you have to prove one of the other sides or angles is congruent first
A = 1/2 bh
like sin^3 A = 8R^3 by extended law of sines
so i did that, top and bottom cancelled out, 8R^3=7
Yes
is that correct?
whats the base whats teh height
Idk how to do it so i come out here to ask
Hi does anyone know how to solve this? I can't even start it :/
@tender prawn
extend AB and draw a line from C straight down to hit line ab
why would you use heron's formula when you know the base and height...
I did not look at the picture lmao I just looked at find area
If you know base and height then you're good
teacher explained in class but i wasnt paying attention :/
pretty sure its something to do w half angle formula
and maybe herons formula
kinda looks like law of cosines
hmm
i like multiplied both sides by s(s-a) and did herons formula and then used a=1/2bc*sinA to get
sinA = s(s-a)(1-cosA)
probably wrong direction tbh
hey can anyone help me
can someone explain this to me rq?
Similar triangles
x= similar triangles?
the top triangle is similar to the whole triangle
and then use side lengths of similar triangles
ok my teacher explained like part of this
i proved the second part using area of triangle = sr
and i think im supposed to somehow relate it to the first but idk how :/
kinda avoiding the half angle formula but it might be that
oh im dumb i turned cot into cos/sin instead of 1/tan and using tan half angle formula
ahh i finally got it lol
i was supposed to use the sum/difference of cot and tan
man trig is hard
help
I know like 10 different ways to do this
but I don't know how to take up every slot
my teacher when she teaches it usually uses every slot
never has one wasted
but all the ways I solved it
didn't use them all
show what you're doing
wait, statement 2 doesn't even make sense
statement 2 doesn't make sense
how
the traversal
makes it true no matter what
wait
that's only if it's parallel
๐
you can't assume that lines c and d are parallel at that stage
that statement is something you could aim to reach
this guy told me that's how I should start it
and then use the converse to justify that the lines are parallel
so how do I start it?
angle 7 congruent to angle 3
?
angle 7 congruent to angle 1
vertical
there are multiply routes you can take
do some angle chasing and apply a converse related to parallel lines
okay
DeMoirvre's
can someone tell me what equation I would need to solve?
well you have (6x-7) do you know what angles on a line add up to
i need help. i have 9-13 questions on a study guide. my test from this study guide is tomorrow. please someone help.
its against the rules to pay for help
oh nvm then
just post your problems and someone will help you
sure can
break $sin 2\theta$ down into $2cos \theta sin \theta$
will that help you at all?
Star_
is it possible to prove this is congruent with the info given
im not sure how to decide if its true or false
if its congruent every side must be equal
can you think of a situation where AC/BC don't necessarily equal EG/GF
Congruence needs one of the following requirements:
- SSS (Side, Side, Side)
Basically if you know all 3 sides are equal in magnitude, they are congruent
-SAS (Side, Angle, Side)
If two pairs of sides are equal in length, and the included angles are equal, then the triangles are congruent, But this one needs the sides to sandwich the angle
-ASA (Angle, Side, Angle) There's another variation of this called AAS
Basically your two given pairs of angles are the same, and the sides are the same
-RHS (Right angle, Hypotenuse, Side)
For right angle triangles only
In your case @zenith garnet you only have 2 pieces of information in your triangles, therefore you cannot reach that conclusion that they are congruent unless I am stoopid
SSA is another variation (but sometimes you cannot prove congruence with it because of the ambiguous case)
and AAA is the only one that you legit cannot use, because that identity only demonstrates similarity, not congruence
hope this helps
Can someone give me the steps in order to prove this trig identity? Not the greatest at Trig functions & identities
Please and thank you๐
sin(2x)/1-cos(2x)= 2/sin(2x)sec^2(x)
Start from RHS
And use half angle identities on both numerator and denominator
Once you simplify it a bit
Use double angle to get your desired result
Not RHS, use LHS
Start off with the Left Side instead?
Yeah
errrr
u get anywhere?
Nah not really
would u like a step through?
yes please
aight give me a moment let me actually solve it myself
Okay thank you
I've only been able to change sin(2x) into 2sin(x)cos(x) -- Double Angle
Do the same for 1-cos(2x)
That's wrong
remember there are 3 options for cos(2x)
Okay yeah thats true
1- cos(2x)= 2 sinยฒ(x)
epic good job
hey
um can someone help me with this?
@raven heart can you find the obtuse angle inside?
and you should use the property that all angles in a triangle adds up to 180 deg
need immediate help
or how you would go about finding it
yep
so can you do that in reverse for your exercise
you just have to find all of the angles in your triangle
and add them up
you also know that by adding up all 3 angles, it will give you 180
which one do you think it is?
i think its the second
and why is that?
only reason why i think that is B and F will the right angles
well you're almost right
if the statement is correct, it means that angle C and angle E are equal, and the same for B and F, A and D
which is true from what we see here
if you say its correct because B and F are equal then its wrong, because there isnt enough evidence
SSS
are you sure?
because as i see it, the first one only talks about a pair of sides
and two pairs of angles
rather than 3 pairs of sides
aas?
oh
what about the second one
i ahve to prive wihich is wrong
yes
so lets find which one is correct first
and then we shall know which one is wrong
ok
i see 2 pairs of sides, and a pair of angles
is that sas?
pay close attention to the positioning
but is it really sas
i dont know.....i mean the angle isnt in the middle of the two sides
youre talking about the first one correct?
yes
so for the second one
to prove that the triangles are congruent,
we have to use angle C
so that means the second one is wrong
yeah
and that info is C
or AB
Any idea of how to solve this?
please ping me
also I was struggling on this question
@slim saddle if DEF ~ JKL, then m<D = m<J
yes
which one has 2 sides and 1 angle?
2nd one?
yes
apply properties of the tan function
as well as trig functions evaluated at special angles
wait
how am i one minute earlier
than you
wait fk im just sht at math
29m is less than 38m
anyways
do squares have legs like trapazoids
wdym by like trapazoids?
never mind
squares are special trapezoids
oh
is this right?
yes
Thatโs what I got
Your given the length of one of the legs which is 9 the and both of the legs are the same length the hypotenuse which is opposite to the right angle sign is equal to 9x2
How would I solve this using law of cosines
Do you know the statement of the law of cosines? Have you gotten any progress in it?
You mean the formula
how do i find a diff restraint?
The formula, and what everything in it means
xยฒ = 13ยฒ + 24ยฒ - 2(13)(24)cos(87ยฐ)
Is that what c is equal to?
Yeah I mean x
That's what xยฒ is equal to anyway
What did you do to get that
xยฒ = 13ยฒ + 24ยฒ - 2(13)(24)cos(87ยฐ)
Cause I did 169 plus 576 equals 745
Which should be the law of cosines, applied to that triangle. Let me know of course if I made any mistake haha
The second part is confusing me what do I do with the cos 87
,w cos(87ยฐ)
Did you distribute -2 by 14 and 24
cos(87) is just a number, approximately 0.05234...
13 not 14
Everything is being multiplied, there's nothing to distribute
So you have the right idea, do every term separately then add them all up in the end
So what do I do with the negative 2 the 13 and the 34 left over
The last term is just
2(13)(24)(0.0523359...)
So -26 times 24 time 0.05
Approximately
I got it now thank you
@molten bronze cant help w/o the question
Can't help w/o the question
Well the first is a given right?
I need help pls help ;-; #geometry-and-trigonometry
post your question
Ohh thank you so much
What are the blanks @west basin
- given 2) bd=bd 3) ???
Sas or hl
Hello:? #geometry-and-trigonometry
Yea I just realized
The angle doesnโt show 90 degrees to
Can I ask one more ?
What are the blank for this one
- pa =ya 3) segment bisector or reflective property?
Idk which
Itโs a multiple choice and they have both tbh
well youd also need to prove its a bisector if you were doing that
Ohhh I guess midpoint isnโt bisecting py
Itโs a point
Just a point I presume
So then it has to be reflexive property
What would 4 be in that case? Sss still right
actually you could use bisector i think
because it gives you the midpoint
i didnt read that
Ahhh so confused
Uhh
I think itโs reflexive still
Cause I feel like with midpoint it canโt bisect
Okay, I have one more
This is my last concern
What are the blanks for this one :?
Just wanna make sure I did it right
what did you put?
- definition of midpoint
Statement 3) angle aix = angle oim
Reason 3 vertical angles
- Sas
looks good to me
Thanks ๐
is this correct
bruh
just use a bunch of supp and corresponding angles
what's a linear pair
for 2 if you're using that as proof you need a few more lines
@upper karma
uh
well read this https://brilliant.org/wiki/polynomial-division/#:~:text=Division with polynomials (done with,a factor of the dividend).
Division with polynomials (done with either long division or synthetic division) is analogous to long division in arithmetic: we take a dividend divided by a divisor to get a quotient and a remainder (which will be zero if the divisor is a factor of the dividend). More formally, given a dividend ...
@upper karma
also this is the wrong channel for this question
put problems 1 by 1
lmao theres no question there????
if everytime you try to make a circle with a compass it makes a spiral is that user error or a bad compass?