anonymous
  • anonymous
Find the value of each variable. If your answer is not an integer, express it in simplest radical form.
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
|dw:1362774575688:dw|
jim_thompson5910
  • jim_thompson5910
is that a 9? or a 4?
anonymous
  • anonymous
9

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

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

Looking for something else?

Not the answer you are looking for? Search for more explanations.