Falco276
  • Falco276
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
schrodinger
  • schrodinger
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Falco276
  • Falco276
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.
Falco276
  • Falco276
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Falco276
  • Falco276

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anonymous
  • anonymous
ok let me see
Falco276
  • Falco276
I think I know. The vertical angle measurement is equal to the horizontal measurement of the right angle.
Falco276
  • Falco276
21 feet by 21 feet. I just have to find out the measurement to rope 2
anonymous
  • anonymous
they are asking you the distance between rope 2 and underneath the balloon right?
Falco276
  • Falco276
yes, exactly.
anonymous
  • anonymous
just to make sure i understood well, i remind you i'm not english!! hehehe
anonymous
  • anonymous
ok
anonymous
  • anonymous
lemme get a paper so i can explain better
Falco276
  • Falco276
|dw:1358712594988:dw|
anonymous
  • anonymous
the distance between rope 2 and 1 is x right? as the drawing says
Falco276
  • Falco276
yes, but I found the half of X which is 45.
Falco276
  • Falco276
look at the drawing, am I right?
Falco276
  • Falco276
I only have to fing the measurement that is the question mark.
Falco276
  • Falco276
*find
anonymous
  • anonymous
you have 2 angles if you notice
anonymous
  • anonymous
even though they dont give you a number, you can see that the angle underneath the balloon is 90, a right triangle
Falco276
  • Falco276
i noticed that.
anonymous
  • anonymous
apply pitagoras
anonymous
  • anonymous
ah well you need to find the sides first, nevermind
Falco276
  • Falco276
sides?
anonymous
  • anonymous
you gonna solve the problem like this
anonymous
  • anonymous
x: distance from rope 2 to underneath the balloon - distance from rope 1 to underneath the balloon
Falco276
  • Falco276
distance from rope 1 to underneath the balloon = 45.
Falco276
  • Falco276
Im trying to figure out rope 2
anonymous
  • anonymous
how do you know its 45? 45 is the given angle
Falco276
  • Falco276
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.
Falco276
  • Falco276
NO NO NO NO!!!!!
anonymous
  • anonymous
Im solving it, wait
Falco276
  • Falco276
I have it wrong!
anonymous
  • anonymous
it has a lot to do with sinus and cosinus
Falco276
  • Falco276
its 21!!!!!! Its 21!!!!
anonymous
  • anonymous
well first you need to remember that sinus = op side / h
anonymous
  • anonymous
we are measuring from rope 1 to balloon now, so sin 30 right?
anonymous
  • anonymous
i tell you that sin 30 = 1/2
anonymous
  • anonymous
so you gonna put 1/2 = 21ft / h right?
anonymous
  • anonymous
solve for h and then you have the hypotenuse
anonymous
  • anonymous
what do you think you can do next
anonymous
  • anonymous
there are many ways to solve this problem
Falco276
  • Falco276
um, okay.
anonymous
  • anonymous
also remember that all the angles of a triangle = 180, if this doesn't happen, it's not a triangle
anonymous
  • anonymous
so if you have a 90º angle, a 30º angle...what's the other angle?
Falco276
  • Falco276
wait, so were trying to find a measurement form rope 1 to the balloon, am I right?
anonymous
  • anonymous
yep
anonymous
  • anonymous
i got it already, just waiting to see how you proceed
anonymous
  • anonymous
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
Falco276
  • Falco276
I never took trigonometery before.
anonymous
  • anonymous
I know you haven't heard of the trigonometric functions
anonymous
  • anonymous
you need to do it 2 steps
Falco276
  • Falco276
no, never. I just take basic geometry.
anonymous
  • anonymous
ok look
anonymous
  • anonymous
|dw:1358713814089:dw|
anonymous
  • anonymous
do you remember what was the sinus and what was the cosinus?
Falco276
  • Falco276
(sigh) I don't remember. (honest, i don't want to be mean to you.)
anonymous
  • anonymous
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
Falco276
  • Falco276
okay, I'll take your note.
anonymous
  • anonymous
|dw:1358714056382:dw|
anonymous
  • anonymous
Now you need to MEMORIZE this scheme, mathematics are also a subject to study!
anonymous
  • anonymous
now ill draw you a triangle and you'll tell me which is the oppsite and which is the adjacent side ok?
Falco276
  • Falco276
ok.
anonymous
  • anonymous
|dw:1358714498016:dw|
Falco276
  • Falco276
I think the opposite side is left from angle A the adj side is right from Angle A.
anonymous
  • anonymous
nope
anonymous
  • anonymous
just read its name
anonymous
  • anonymous
opposite = infront of the angle
anonymous
  • anonymous
adjacent = sidewards the angle
anonymous
  • anonymous
alongside of it
Falco276
  • Falco276
fine! Isn't the adjecent side the- How do I Explain it! Isnt the adjecent side the sidewards of the angle?
anonymous
  • anonymous
draw it
Falco276
  • Falco276
|dw:1358715165594:dw|
anonymous
  • anonymous
no, the other one, that's the hypotenuse
Falco276
  • Falco276
|dw:1358715296994:dw|
Falco276
  • Falco276
anonymous
  • anonymous
yep
hba
  • hba
Falco276
  • Falco276
@hba please help me!
hba
  • hba
@GCR92 is helping you,Just follow him :)
anonymous
  • anonymous
I have to explain the whole trigonometry before you are able to solve that problem...
Falco276
  • Falco276
(sigh) ok.
anonymous
  • anonymous
I explain as simple as it is, but not simpler
Falco276
  • Falco276
ok
anonymous
  • anonymous
ok i put the turbo now
anonymous
  • anonymous
we are going to solve 2 triangles
anonymous
  • anonymous
|dw:1358715724015:dw|
Falco276
  • Falco276
wait. I think I have it.
anonymous
  • anonymous
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
Falco276
  • Falco276
For the 45° triangle
anonymous
  • anonymous
and sinus = op side / h
anonymous
  • anonymous
and we can make a relationship
anonymous
  • anonymous
an equation
Falco276
  • Falco276
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
Falco276
  • Falco276
is this correct?
anonymous
  • anonymous
where did you get 15?
Falco276
  • Falco276
oh, no i meant 21 (facepalm)
anonymous
  • anonymous
You could've done it if you had the value of the x side
anonymous
  • anonymous
but that's what we are looking for
anonymous
  • anonymous
to use the tangent you need to have the value of 2 sides
anonymous
  • anonymous
I'd like to continue now
Falco276
  • Falco276
|dw:1358716138389:dw|
anonymous
  • anonymous
why?
Falco276
  • Falco276
|dw:1358716271703:dw|
Falco276
  • Falco276
|dw:1358716355941:dw|
Falco276
  • Falco276
now we take the other triangle.
anonymous
  • anonymous
the adjacent side is not 21, 21 is the only data they give us, you can't invent it
anonymous
  • anonymous
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
anonymous
  • anonymous
sin 30 = 1/2, we do that in order to calculate H
anonymous
  • anonymous
1/2 = 21 / h
anonymous
  • anonymous
h= 42
anonymous
  • anonymous
now we take the cosinus in order to calculate X
anonymous
  • anonymous
cos 30 = sqrt 3 / 2
anonymous
  • anonymous
sqrt 3 / 2 = 42 / x
anonymous
  • anonymous
x = 36.373
Falco276
  • Falco276
|dw:1358716402610:dw|
Falco276
  • Falco276
|dw:1358717381175:dw|
Falco276
  • Falco276
|dw:1358717481086:dw|
anonymous
  • anonymous
you can never write tan and let it alone
anonymous
  • anonymous
it is always tan OF SOMETHING
anonymous
  • anonymous
tan of x, tan of alfa, tan of 20
Falco276
  • Falco276
so the answer is 21 sq. root 3
anonymous
  • anonymous
ill solve it
anonymous
  • anonymous
2 triangles
anonymous
  • anonymous
take the 30º triangle and then, sin 30 = 1/2
anonymous
  • anonymous
1/2 = 21 / h, h = 42
anonymous
  • anonymous
now we have the h of the first triangle
anonymous
  • anonymous
now we can calculate the distance from the rope to underneath the balloon, that distance will be given by the cosinus
anonymous
  • anonymous
cos 30 = sqrt 3 / 2
anonymous
  • anonymous
sqrt 3 /2 = x/42
anonymous
  • anonymous
x = 36,373
anonymous
  • anonymous
now we go to the second triangle and apply exactly the same steps but with 45º
Falco276
  • Falco276
maybe my way of solving this problem was wrong. sorry.
Falco276
  • Falco276
i tried my best.
anonymous
  • anonymous
I know but mathematics doesn't magically happen, you need to study a lot( and suffer lol) dont worry
anonymous
  • anonymous
if you do the same with the second triangle
anonymous
  • anonymous
sin 45 = sqrt 2 / 2
anonymous
  • anonymous
sqrt 2 / 2 = 21 / h
anonymous
  • anonymous
h = 29.698
anonymous
  • anonymous
now we calculate the cosinus
anonymous
  • anonymous
cos 45 = sqrt 2 / 2
anonymous
  • anonymous
sqrt 2 / 2 = x / 28,698
anonymous
  • anonymous
x = 20,292
anonymous
  • anonymous
distance from underneath the ballon to the second rope = 36, 373 + 20,292 = 56,665 feet
anonymous
  • anonymous
and it's solved
Falco276
  • Falco276
wait, but earlier you said that x is 36- never mind :P
anonymous
  • anonymous
that's the distance between underneath the balloon and rope 2
Falco276
  • Falco276
ah, i see.
anonymous
  • anonymous
and 20,292 ft is the distance between underneath the balloon and rope 1
anonymous
  • anonymous
sorry
Falco276
  • Falco276
got it.
anonymous
  • anonymous
36ft is the distance between rope 2 and 1
anonymous
  • anonymous
then you calculate from rope 1 to underneath the ballon and it gives you 20 ft
anonymous
  • anonymous
you add it and you obtain the final result
Falco276
  • Falco276
okay.
anonymous
  • anonymous
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!
anonymous
  • anonymous
needed*
anonymous
  • anonymous
you did well! at least you had ideas! you only need to learn the theory well
anonymous
  • anonymous
i also think your teachers are crazy though
Falco276
  • Falco276
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.
anonymous
  • anonymous
You are welcome, sure, see you! :D
Falco276
  • Falco276
thanks! (thumbs up)
anonymous
  • anonymous
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
Falco276
  • Falco276
oh, i understand, dont worry! my teachers are really nice.

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