Find the value of each variable. If your answer is not an integer, express it in simplest radical form.

- anonymous

- jamiebookeater

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- anonymous

|dw:1362774575688:dw|

- jim_thompson5910

is that a 9? or a 4?

- anonymous

9

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## More answers

- jim_thompson5910

ok thanks

- jim_thompson5910

here's the template again
|dw:1362774782473:dw|
I would add this to your notes if you don't have it already

- jim_thompson5910

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

- anonymous

how did you get 30 and 2x?

- jim_thompson5910

well the given angle is 60, which adds to the right angle 90 to get 90+60 = 150
the remaining angle must be 30 in order for the three to add to 180

- jim_thompson5910

since 150 + 30 = 180

- jim_thompson5910

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

- jim_thompson5910

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

- anonymous

should I write that process down?

- jim_thompson5910

yes I would if you're not familiar with it

- anonymous

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

- jim_thompson5910

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

- jim_thompson5910

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

- jim_thompson5910

when you match up the terms

- anonymous

why did you get rid of the 9?

- jim_thompson5910

what do you mean?

- anonymous

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

- jim_thompson5910

no, I said x was 9
so x = 9

- jim_thompson5910

oh i see what you mean

- anonymous

you said in the picture above..

- jim_thompson5910

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

- jim_thompson5910

notice how the x and the 9 match up

- anonymous

oh.

- jim_thompson5910

so that's how I got that x = 9

- jim_thompson5910

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

- anonymous

you are so confusing me. Can you write it out like, step 1, step 2. And start from the beginning cause I'm lost

- jim_thompson5910

did you see how I got x = 9?

- jim_thompson5910

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

- jim_thompson5910

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

- anonymous

can we not use the template? it's confusing

- jim_thompson5910

have you learned trig yet?

- anonymous

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

- jim_thompson5910

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

- anonymous

I just wanna solve it..

- jim_thompson5910

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

- jim_thompson5910

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

- anonymous

I think

- jim_thompson5910

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

- jim_thompson5910

I'll assume yes

- jim_thompson5910

tan(30) = opposite/adjacent
tan(30) = x/(9*sqrt(3))
sqrt(3)/3 = x/(9*sqrt(3)) ... use a calculator or the unit circle here
sqrt(3)*9*sqrt(3) = 3x
9*sqrt(3)*sqrt(3) = 3x
9*3 = 3x
27 = 3x
3x = 27
x = 27/3
x = 9
so you can see that we get the same answer as we did before

- jim_thompson5910

sure this method is a bit more complicated, but it works
it all hinges on whether you know trig or not

- anonymous

do I write that down?

- jim_thompson5910

yeah, or you could skip a few steps I guess

- jim_thompson5910

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

- anonymous

Should I write this down and skip all the other steps? :)
sqrt(3)*9*sqrt(3) = 3x
9*sqrt(3)*sqrt(3) = 3x
9*3 = 3x
27 = 3x
3x = 27
x = 27/3
x = 9

- jim_thompson5910

I would have the previous steps in there, these ones
tan(30) = opposite/adjacent
tan(30) = x/(9*sqrt(3))
sqrt(3)/3 = x/(9*sqrt(3))
-------------------------------------------------------
I guess you could skip step 2 to get just these steps
tan(30) = opposite/adjacent
sqrt(3)/3 = x/(9*sqrt(3))

- anonymous

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

- jim_thompson5910

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

- anonymous

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

- jim_thompson5910

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

- anonymous

I got the x. What's the Y?

- anonymous

@jim_thompson5910

- jim_thompson5910

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

- jim_thompson5910

so y = 18

- jim_thompson5910

you can use the pythagorean theorem to confirm, but you'd get the same answer (just in a more complicated way)

- anonymous

how did you find that Y= 2x?

- jim_thompson5910

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

- jim_thompson5910

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

- jim_thompson5910

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

- anonymous

y=18?

- jim_thompson5910

yes good

- anonymous

okay, 2nd problem! :p

- anonymous

Recreation. A skateboarding ramp is 12 inches high and rises at an angle of 17 degrees. How long is the base of the ramp? Round to the nearest inch.

- anonymous

@jim_thompson5910

- jim_thompson5910

|dw:1362781717017:dw|

- jim_thompson5910

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

- anonymous

do you not know X?

- anonymous

@jim_thompson5910

- jim_thompson5910

not until you solve for it

- jim_thompson5910

by typing 12/tan(17) into the calculator

- anonymous

oh lol

- jim_thompson5910

yeah it's not too bad to find

- anonymous

39.25

- jim_thompson5910

yep

- anonymous

so, that's the answer?

- jim_thompson5910

yes it is

- anonymous

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

- jim_thompson5910

ok works for us lol

- anonymous

The lengths of the diagonals of a rhombus are in 2 inches and 5 inches. Find the measures of the angles of the rhombus to the nearest degree.

- jim_thompson5910

|dw:1362782836744:dw|

- jim_thompson5910

|dw:1362782951298:dw|

- jim_thompson5910

we get this triangle
|dw:1362782979724:dw|

- jim_thompson5910

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

- jim_thompson5910

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

- anonymous

do I draw all of these?

- jim_thompson5910

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

- anonymous

okay

- jim_thompson5910

so what do you get for x?

- anonymous

wait, what's arctan?

- jim_thompson5910

it's the inverse of tangent

- jim_thompson5910

if you don't have a calculator that can handle arctan, then look here
http://www.google.com/search?hl=&q=arctan%280.4%29+in+degrees&sourceid=navclient-ff&rlz=1B3GGLL_enUS420US420&ie=UTF-8

- anonymous

how do I get it on my calculator?

- jim_thompson5910

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

- jim_thompson5910

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

- anonymous

where's arc on the calculator?

- jim_thompson5910

what kind of calculator do you have?

- anonymous

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

- anonymous

But I still got the right answer

- jim_thompson5910

oh same thing

- jim_thompson5910

atan is just a shorter version of arctan

- anonymous

thankyou.
:-)

- jim_thompson5910

np what did you get for x?

- anonymous

21.8

- anonymous

btw, do I find Y?

- jim_thompson5910

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

- jim_thompson5910

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

- jim_thompson5910

21.8*2 = 43.6 which is the measure of one set of angles of the rhombus
68.2*2 = 136.4 which is the measure of another set of angles of the rhombus

- anonymous

Add X and Y?

- jim_thompson5910

what do you mean

- anonymous

oh..double them seperately.

- jim_thompson5910

yes

- jim_thompson5910

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

- anonymous

okay, what do I do after?

- jim_thompson5910

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

- anonymous

oh, so x= 43.6 and y=136.4?

- jim_thompson5910

no those are the two angles of a rhombus

- jim_thompson5910

the other two are congruent to those two

- jim_thompson5910

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

- anonymous

should I draw that?

- jim_thompson5910

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

- jim_thompson5910

no, they just want the angles

- jim_thompson5910

you can if you want

- anonymous

where are the diagonals?

- jim_thompson5910

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

- jim_thompson5910

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

- anonymous

yeah

- anonymous

so, I'm done now?

- jim_thompson5910

yes pretty much

- anonymous

:D YAYAYAYAYAY

- jim_thompson5910

lol

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