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|dw:1362774575688:dw|

is that a 9? or a 4?

ok thanks

notice how the number in front of the sqrt(3) on the longer leg is 9
so that must mean that x = 9

how did you get 30 and 2x?

since 150 + 30 = 180

as for the 2x...
the hypotenuse is always twice as long as the shorter leg in a 30-60-90 triangle

so that explains the x for the shorter leg and 2x for the hypotenuse

should I write that process down?

yes I would if you're not familiar with it

would it be a good idea to write it on my homework?

if you want to, there's nothing wrong with using this template

you can draw the template off to the side and show that x must be 9

when you match up the terms

why did you get rid of the 9?

what do you mean?

it was 9 sqrt 3? now, it's X sqrt 3?

no, I said x was 9
so x = 9

oh i see what you mean

you said in the picture above..

9 * sqrt(3) ... what we're given
x * sqrt(3)... template

notice how the x and the 9 match up

oh.

so that's how I got that x = 9

the y and the 2x match up, so
y = 2x
y = 2*9
y = 18

did you see how I got x = 9?

here is your triangle (on top) and the general template triangle (on bottom)
|dw:1362776258556:dw|

notice how these two sides match up
|dw:1362776369974:dw|

can we not use the template? it's confusing

have you learned trig yet?

can you just show me the process of how to solve this?

I'm just curious because if you have, then we can use that

I just wanna solve it..

I know, but I need to know if you know trig so it will make sense if I use it

have you learned things like sine, cosine, tangent, etc?

I think

so you've seen things like
sine = opposite/hypotenuse
?

I'll assume yes

do I write that down?

yeah, or you could skip a few steps I guess

wherever you see a 'sqrt', use the square root symbol of course

I'm confused. Is this 3 times 9? sqrt(3)*9*sqrt(3) = 3x

yeah it's just a complicated way of saying 9*3

so it's actually 9 times 3 sqrt 3= 3x

no the sqrt(3) terms multiply to 3
so that's why
9*sqrt(3)*sqrt(3) = 3x
turns into
9*3 = 3x

I got the x. What's the Y?

well y = 2x
so y = 2*9 = 18

so y = 18

how did you find that Y= 2x?

well you would use the template...but just remembered you don't like that template very much

so you can use
a^2 + b^2 = c^2
to find the value of y

a^2 + b^2 = c^2
9^2 + (9*sqrt(3))^2 = y^2
81 + 243 = y^2
keep going to solve for y

y=18?

yes good

okay, 2nd problem! :p

|dw:1362781717017:dw|

tan(17) = 12/x
x*tan(17) = 12
x = 12/tan(17)
x = ???

do you not know X?

not until you solve for it

by typing 12/tan(17) into the calculator

oh lol

yeah it's not too bad to find

39.25

yep

so, that's the answer?

yes it is

Last question. I was wrong btw. There's only 3 questions left, not 4. :P

ok works for us lol

|dw:1362782836744:dw|

|dw:1362782951298:dw|

we get this triangle
|dw:1362782979724:dw|

let x and y be the two unknown angles
|dw:1362783041003:dw|

tan(x) = 1/2.5
tan(x) = 0.4
x = arctan(0.4)
x = ??

do I draw all of these?

you don't have to, but it helps to see how to get the answer

okay

so what do you get for x?

wait, what's arctan?

it's the inverse of tangent

how do I get it on my calculator?

at the top, you'll see that " arctan(0.4) = 21.8014095 degrees"

if you have a TI-83, 85, 86, etc
you can hit 2nd, then tan to get arctan

where's arc on the calculator?

what kind of calculator do you have?

it said "Atan" when i did that, not arctan

But I still got the right answer

oh same thing

atan is just a shorter version of arctan

thankyou.
:-)

np what did you get for x?

21.8

btw, do I find Y?

y = 90 - x
y = 90 - 21.8
y = 68.2

now that you know x and y, you would double them to find the angles of the rhombus

Add X and Y?

what do you mean

oh..double them seperately.

yes

because we want the angles of the rhombus, not the triangle

okay, what do I do after?

you're done, you found the angles of the rhombus

oh, so x= 43.6 and y=136.4?

no those are the two angles of a rhombus

the other two are congruent to those two

we have something like this
|dw:1362784125897:dw|

should I draw that?

the diagonals are 5 and 2, I just didn't have enough room to draw them in

no, they just want the angles

you can if you want

where are the diagonals?

lol like i said, i didn't have enough room

|dw:1362784257953:dw|
see how things get cut off?

yeah

so, I'm done now?

yes pretty much

:D YAYAYAYAYAY

lol