Emily778
Find the value of each variable. If your answer is not an integer, express it in simplest radical form.
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Emily778
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|dw:1362774575688:dw|
jim_thompson5910
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is that a 9? or a 4?
Emily778
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9
jim_thompson5910
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ok thanks
jim_thompson5910
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here's the template again
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I would add this to your notes if you don't have it already
jim_thompson5910
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notice how the number in front of the sqrt(3) on the longer leg is 9
so that must mean that x = 9
Emily778
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how did you get 30 and 2x?
jim_thompson5910
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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
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since 150 + 30 = 180
jim_thompson5910
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as for the 2x...
the hypotenuse is always twice as long as the shorter leg in a 30-60-90 triangle
jim_thompson5910
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so that explains the x for the shorter leg and 2x for the hypotenuse
Emily778
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should I write that process down?
jim_thompson5910
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yes I would if you're not familiar with it
Emily778
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would it be a good idea to write it on my homework?
jim_thompson5910
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if you want to, there's nothing wrong with using this template
jim_thompson5910
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you can draw the template off to the side and show that x must be 9
jim_thompson5910
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when you match up the terms
Emily778
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why did you get rid of the 9?
jim_thompson5910
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what do you mean?
Emily778
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it was 9 sqrt 3? now, it's X sqrt 3?
jim_thompson5910
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no, I said x was 9
so x = 9
jim_thompson5910
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oh i see what you mean
Emily778
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you said in the picture above..
jim_thompson5910
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9 * sqrt(3) ... what we're given
x * sqrt(3)... template
jim_thompson5910
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notice how the x and the 9 match up
Emily778
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oh.
jim_thompson5910
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so that's how I got that x = 9
jim_thompson5910
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the y and the 2x match up, so
y = 2x
y = 2*9
y = 18
Emily778
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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
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did you see how I got x = 9?
jim_thompson5910
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here is your triangle (on top) and the general template triangle (on bottom)
|dw:1362776258556:dw|
jim_thompson5910
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notice how these two sides match up
|dw:1362776369974:dw|
Emily778
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can we not use the template? it's confusing
jim_thompson5910
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have you learned trig yet?
Emily778
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can you just show me the process of how to solve this?
jim_thompson5910
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I'm just curious because if you have, then we can use that
Emily778
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I just wanna solve it..
jim_thompson5910
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I know, but I need to know if you know trig so it will make sense if I use it
jim_thompson5910
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have you learned things like sine, cosine, tangent, etc?
Emily778
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I think
jim_thompson5910
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so you've seen things like
sine = opposite/hypotenuse
?
jim_thompson5910
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I'll assume yes
jim_thompson5910
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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
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sure this method is a bit more complicated, but it works
it all hinges on whether you know trig or not
Emily778
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do I write that down?
jim_thompson5910
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yeah, or you could skip a few steps I guess
jim_thompson5910
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wherever you see a 'sqrt', use the square root symbol of course
Emily778
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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
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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))
Emily778
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I'm confused. Is this 3 times 9? sqrt(3)*9*sqrt(3) = 3x
jim_thompson5910
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yeah it's just a complicated way of saying 9*3
Emily778
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so it's actually 9 times 3 sqrt 3= 3x
jim_thompson5910
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no the sqrt(3) terms multiply to 3
so that's why
9*sqrt(3)*sqrt(3) = 3x
turns into
9*3 = 3x
Emily778
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I got the x. What's the Y?
Emily778
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@jim_thompson5910
jim_thompson5910
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well y = 2x
so y = 2*9 = 18
jim_thompson5910
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so y = 18
jim_thompson5910
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you can use the pythagorean theorem to confirm, but you'd get the same answer (just in a more complicated way)
Emily778
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how did you find that Y= 2x?
jim_thompson5910
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well you would use the template...but just remembered you don't like that template very much
jim_thompson5910
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so you can use
a^2 + b^2 = c^2
to find the value of y
jim_thompson5910
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a^2 + b^2 = c^2
9^2 + (9*sqrt(3))^2 = y^2
81 + 243 = y^2
keep going to solve for y
Emily778
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y=18?
jim_thompson5910
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yes good
Emily778
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okay, 2nd problem! :p
Emily778
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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.
Emily778
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@jim_thompson5910
jim_thompson5910
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|dw:1362781717017:dw|
jim_thompson5910
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tan(17) = 12/x
x*tan(17) = 12
x = 12/tan(17)
x = ???
Emily778
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do you not know X?
Emily778
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@jim_thompson5910
jim_thompson5910
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not until you solve for it
jim_thompson5910
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by typing 12/tan(17) into the calculator
Emily778
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oh lol
jim_thompson5910
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yeah it's not too bad to find
Emily778
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39.25
Emily778
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so, that's the answer?
jim_thompson5910
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yes it is
Emily778
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Last question. I was wrong btw. There's only 3 questions left, not 4. :P
jim_thompson5910
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ok works for us lol
Emily778
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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
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|dw:1362782836744:dw|
jim_thompson5910
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|dw:1362782951298:dw|
jim_thompson5910
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we get this triangle
|dw:1362782979724:dw|
jim_thompson5910
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let x and y be the two unknown angles
|dw:1362783041003:dw|
jim_thompson5910
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tan(x) = 1/2.5
tan(x) = 0.4
x = arctan(0.4)
x = ??
Emily778
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do I draw all of these?
jim_thompson5910
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you don't have to, but it helps to see how to get the answer
Emily778
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okay
jim_thompson5910
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so what do you get for x?
Emily778
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wait, what's arctan?
jim_thompson5910
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it's the inverse of tangent
Emily778
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how do I get it on my calculator?
jim_thompson5910
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at the top, you'll see that " arctan(0.4) = 21.8014095 degrees"
jim_thompson5910
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if you have a TI-83, 85, 86, etc
you can hit 2nd, then tan to get arctan
Emily778
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where's arc on the calculator?
jim_thompson5910
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what kind of calculator do you have?
Emily778
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it said "Atan" when i did that, not arctan
Emily778
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But I still got the right answer
jim_thompson5910
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oh same thing
jim_thompson5910
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atan is just a shorter version of arctan
Emily778
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thankyou.
:-)
jim_thompson5910
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np what did you get for x?
Emily778
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21.8
Emily778
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btw, do I find Y?
jim_thompson5910
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y = 90 - x
y = 90 - 21.8
y = 68.2
jim_thompson5910
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now that you know x and y, you would double them to find the angles of the rhombus
jim_thompson5910
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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
Emily778
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Add X and Y?
jim_thompson5910
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what do you mean
Emily778
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oh..double them seperately.
jim_thompson5910
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because we want the angles of the rhombus, not the triangle
Emily778
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okay, what do I do after?
jim_thompson5910
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you're done, you found the angles of the rhombus
Emily778
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oh, so x= 43.6 and y=136.4?
jim_thompson5910
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no those are the two angles of a rhombus
jim_thompson5910
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the other two are congruent to those two
jim_thompson5910
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we have something like this
|dw:1362784125897:dw|
Emily778
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should I draw that?
jim_thompson5910
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the diagonals are 5 and 2, I just didn't have enough room to draw them in
jim_thompson5910
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no, they just want the angles
jim_thompson5910
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you can if you want
Emily778
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where are the diagonals?
jim_thompson5910
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lol like i said, i didn't have enough room
jim_thompson5910
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|dw:1362784257953:dw|
see how things get cut off?
Emily778
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yeah
Emily778
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so, I'm done now?
jim_thompson5910
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yes pretty much
Emily778
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:D YAYAYAYAYAY