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There are many ropes keeping a hot air balloon from floating away before a balloon race. One of these ropes is fixed to the ground at a 45° angle. Another is fixed to the ground at a 30° angle.

Mathematics
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If the hot air balloon is 21 feet off the ground, what is the distance between the ground directly underneath the balloon and the second rope rounded to the nearest hundredth of a foot? Type the numeric answer only in the box below.
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Other answers:

ok let me see
I think I know. The vertical angle measurement is equal to the horizontal measurement of the right angle.
21 feet by 21 feet. I just have to find out the measurement to rope 2
they are asking you the distance between rope 2 and underneath the balloon right?
yes, exactly.
just to make sure i understood well, i remind you i'm not english!! hehehe
ok
lemme get a paper so i can explain better
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the distance between rope 2 and 1 is x right? as the drawing says
yes, but I found the half of X which is 45.
look at the drawing, am I right?
I only have to fing the measurement that is the question mark.
*find
you have 2 angles if you notice
even though they dont give you a number, you can see that the angle underneath the balloon is 90, a right triangle
i noticed that.
apply pitagoras
ah well you need to find the sides first, nevermind
sides?
you gonna solve the problem like this
x: distance from rope 2 to underneath the balloon - distance from rope 1 to underneath the balloon
distance from rope 1 to underneath the balloon = 45.
Im trying to figure out rope 2
how do you know its 45? 45 is the given angle
no, not from the angle. On how I got 45 was that the vertical measurement leading to the balloon has the same measurement that leads to rope 1.
NO NO NO NO!!!!!
Im solving it, wait
I have it wrong!
it has a lot to do with sinus and cosinus
its 21!!!!!! Its 21!!!!
well first you need to remember that sinus = op side / h
we are measuring from rope 1 to balloon now, so sin 30 right?
i tell you that sin 30 = 1/2
so you gonna put 1/2 = 21ft / h right?
solve for h and then you have the hypotenuse
what do you think you can do next
there are many ways to solve this problem
um, okay.
also remember that all the angles of a triangle = 180, if this doesn't happen, it's not a triangle
so if you have a 90º angle, a 30º angle...what's the other angle?
wait, so were trying to find a measurement form rope 1 to the balloon, am I right?
yep
i got it already, just waiting to see how you proceed
that problem is too difficult for you, i mean, they should teach you trigonommetry first, there's no way you can do that without using trigonommetry
I never took trigonometery before.
I know you haven't heard of the trigonometric functions
you need to do it 2 steps
no, never. I just take basic geometry.
ok look
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do you remember what was the sinus and what was the cosinus?
(sigh) I don't remember. (honest, i don't want to be mean to you.)
hahaha, dont worry about it, i'll explain again, but you should take note of it because you are going to need it in EVERY problem
okay, I'll take your note.
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Now you need to MEMORIZE this scheme, mathematics are also a subject to study!
now ill draw you a triangle and you'll tell me which is the oppsite and which is the adjacent side ok?
ok.
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I think the opposite side is left from angle A the adj side is right from Angle A.
nope
just read its name
opposite = infront of the angle
adjacent = sidewards the angle
alongside of it
fine! Isn't the adjecent side the- How do I Explain it! Isnt the adjecent side the sidewards of the angle?
draw it
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no, the other one, that's the hypotenuse
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yep
  • hba
@hba please help me!
  • hba
@GCR92 is helping you,Just follow him :)
I have to explain the whole trigonometry before you are able to solve that problem...
(sigh) ok.
I explain as simple as it is, but not simpler
ok
ok i put the turbo now
we are going to solve 2 triangles
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wait. I think I have it.
we are going to use the sinus to solve this one, why sinus? because the problem has given us the opposite side, wich is 21 ft
For the 45° triangle
and sinus = op side / h
and we can make a relationship
an equation
tan Ө = opposite / adjacent tan Ө = height of the balloon off the ground / x tan 45° = 15 / x x = 15 / tan 45° x = 15 / 1 x = 15
is this correct?
where did you get 15?
oh, no i meant 21 (facepalm)
You could've done it if you had the value of the x side
but that's what we are looking for
to use the tangent you need to have the value of 2 sides
I'd like to continue now
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why?
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now we take the other triangle.
the adjacent side is not 21, 21 is the only data they give us, you can't invent it
listen i dont want to be mean either but i want to help you and i want to finish, if you think you don't need to do what i tell you to solve it, go ahead
sin 30 = 1/2, we do that in order to calculate H
1/2 = 21 / h
h= 42
now we take the cosinus in order to calculate X
cos 30 = sqrt 3 / 2
sqrt 3 / 2 = 42 / x
x = 36.373
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you can never write tan and let it alone
it is always tan OF SOMETHING
tan of x, tan of alfa, tan of 20
so the answer is 21 sq. root 3
ill solve it
2 triangles
take the 30º triangle and then, sin 30 = 1/2
1/2 = 21 / h, h = 42
now we have the h of the first triangle
now we can calculate the distance from the rope to underneath the balloon, that distance will be given by the cosinus
cos 30 = sqrt 3 / 2
sqrt 3 /2 = x/42
x = 36,373
now we go to the second triangle and apply exactly the same steps but with 45º
maybe my way of solving this problem was wrong. sorry.
i tried my best.
I know but mathematics doesn't magically happen, you need to study a lot( and suffer lol) dont worry
if you do the same with the second triangle
sin 45 = sqrt 2 / 2
sqrt 2 / 2 = 21 / h
h = 29.698
now we calculate the cosinus
cos 45 = sqrt 2 / 2
sqrt 2 / 2 = x / 28,698
x = 20,292
distance from underneath the ballon to the second rope = 36, 373 + 20,292 = 56,665 feet
and it's solved
wait, but earlier you said that x is 36- never mind :P
that's the distance between underneath the balloon and rope 2
ah, i see.
and 20,292 ft is the distance between underneath the balloon and rope 1
sorry
got it.
36ft is the distance between rope 2 and 1
then you calculate from rope 1 to underneath the ballon and it gives you 20 ft
you add it and you obtain the final result
okay.
what i did is totally useless, i mean you can't learn in 20 min, i always believed that a teacher is need in order to learn something, anyway, wish you luck with this!
needed*
you did well! at least you had ideas! you only need to learn the theory well
i also think your teachers are crazy though
XD Thanks Gonzalo! I promise to keep the theory at heart. Yes, I finally understood the answer and also the work. I'll tell you if need help on anything else.
You are welcome, sure, see you! :D
thanks! (thumbs up)
I also can be wrong, i mean if your teachers yells at you it is my fault, just don't take that in account, it's been ages since i dont take trigonometry :p
oh, i understand, dont worry! my teachers are really nice.

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