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.

- Falco276

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- 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

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- Falco276

@GCR92

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- anonymous

ok let me see

- Falco276

I think I know.
The vertical angle measurement is equal to the horizontal measurement of the right angle.

- Falco276

21 feet by 21 feet.
I just have to find out the measurement to rope 2

- anonymous

they are asking you the distance between rope 2 and underneath the balloon right?

- Falco276

yes, exactly.

- anonymous

just to make sure i understood well, i remind you i'm not english!! hehehe

- anonymous

ok

- anonymous

lemme get a paper so i can explain better

- Falco276

|dw:1358712594988:dw|

- anonymous

the distance between rope 2 and 1 is x right? as the drawing says

- Falco276

yes, but I found the half of X which is 45.

- Falco276

look at the drawing, am I right?

- Falco276

I only have to fing the measurement that is the question mark.

- Falco276

*find

- anonymous

you have 2 angles if you notice

- anonymous

even though they dont give you a number, you can see that the angle underneath the balloon is 90, a right triangle

- Falco276

i noticed that.

- anonymous

apply pitagoras

- anonymous

ah well you need to find the sides first, nevermind

- Falco276

sides?

- anonymous

you gonna solve the problem like this

- anonymous

x: distance from rope 2 to underneath the balloon - distance from rope 1 to underneath the balloon

- Falco276

distance from rope 1 to underneath the balloon = 45.

- Falco276

Im trying to figure out rope 2

- anonymous

how do you know its 45? 45 is the given angle

- 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

NO NO NO NO!!!!!

- anonymous

Im solving it, wait

- Falco276

I have it wrong!

- anonymous

it has a lot to do with sinus and cosinus

- Falco276

its 21!!!!!!
Its 21!!!!

- anonymous

well first you need to remember that sinus = op side / h

- anonymous

we are measuring from rope 1 to balloon now, so sin 30 right?

- anonymous

i tell you that sin 30 = 1/2

- anonymous

so you gonna put 1/2 = 21ft / h right?

- anonymous

solve for h and then you have the hypotenuse

- anonymous

what do you think you can do next

- anonymous

there are many ways to solve this problem

- Falco276

um, okay.

- anonymous

also remember that all the angles of a triangle = 180, if this doesn't happen, it's not a triangle

- anonymous

so if you have a 90º angle, a 30º angle...what's the other angle?

- Falco276

wait, so were trying to find a measurement form rope 1 to the balloon, am I right?

- anonymous

yep

- anonymous

i got it already, just waiting to see how you proceed

- 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

I never took trigonometery before.

- anonymous

I know you haven't heard of the trigonometric functions

- anonymous

you need to do it 2 steps

- Falco276

no, never. I just take basic geometry.

- anonymous

ok look

- anonymous

|dw:1358713814089:dw|

- anonymous

do you remember what was the sinus and what was the cosinus?

- Falco276

(sigh)
I don't remember. (honest, i don't want to be mean to you.)

- 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

okay, I'll take your note.

- anonymous

|dw:1358714056382:dw|

- anonymous

Now you need to MEMORIZE this scheme, mathematics are also a subject to study!

- anonymous

now ill draw you a triangle and you'll tell me which is the oppsite and which is the adjacent side ok?

- Falco276

ok.

- anonymous

|dw:1358714498016:dw|

- Falco276

I think the opposite side is left from angle A
the adj side is right from Angle A.

- anonymous

nope

- anonymous

just read its name

- anonymous

opposite = infront of the angle

- anonymous

adjacent = sidewards the angle

- anonymous

alongside of it

- Falco276

fine! Isn't the adjecent side the- How do I Explain it!
Isnt the adjecent side the sidewards of the angle?

- anonymous

draw it

- Falco276

|dw:1358715165594:dw|

- anonymous

no, the other one, that's the hypotenuse

- Falco276

|dw:1358715296994:dw|

- Falco276

@hba

- anonymous

yep

- hba

Yes @Falco276

- Falco276

@hba
please help me!

- hba

@GCR92 is helping you,Just follow him :)

- anonymous

I have to explain the whole trigonometry before you are able to solve that problem...

- Falco276

(sigh)
ok.

- anonymous

I explain as simple as it is, but not simpler

- Falco276

ok

- anonymous

ok i put the turbo now

- anonymous

we are going to solve 2 triangles

- anonymous

|dw:1358715724015:dw|

- Falco276

wait. I think I have it.

- 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

For the 45° triangle

- anonymous

and sinus = op side / h

- anonymous

and we can make a relationship

- anonymous

an equation

- 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

is this correct?

- anonymous

where did you get 15?

- Falco276

oh, no i meant 21
(facepalm)

- anonymous

You could've done it if you had the value of the x side

- anonymous

but that's what we are looking for

- anonymous

to use the tangent you need to have the value of 2 sides

- anonymous

I'd like to continue now

- Falco276

|dw:1358716138389:dw|

- anonymous

why?

- Falco276

|dw:1358716271703:dw|

- Falco276

|dw:1358716355941:dw|

- Falco276

now we take the other triangle.

- anonymous

the adjacent side is not 21, 21 is the only data they give us, you can't invent it

- 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

sin 30 = 1/2, we do that in order to calculate H

- anonymous

1/2 = 21 / h

- anonymous

h= 42

- anonymous

now we take the cosinus in order to calculate X

- anonymous

cos 30 = sqrt 3 / 2

- anonymous

sqrt 3 / 2 = 42 / x

- anonymous

x = 36.373

- Falco276

|dw:1358716402610:dw|

- Falco276

|dw:1358717381175:dw|

- Falco276

|dw:1358717481086:dw|

- anonymous

you can never write tan and let it alone

- anonymous

it is always tan OF SOMETHING

- anonymous

tan of x, tan of alfa, tan of 20

- Falco276

so the answer is 21 sq. root 3

- anonymous

ill solve it

- anonymous

2 triangles

- anonymous

take the 30º triangle and then, sin 30 = 1/2

- anonymous

1/2 = 21 / h, h = 42

- anonymous

now we have the h of the first triangle

- anonymous

now we can calculate the distance from the rope to underneath the balloon, that distance will be given by the cosinus

- anonymous

cos 30 = sqrt 3 / 2

- anonymous

sqrt 3 /2 = x/42

- anonymous

x = 36,373

- anonymous

now we go to the second triangle and apply exactly the same steps but with 45º

- Falco276

maybe my way of solving this problem was wrong.
sorry.

- Falco276

i tried my best.

- anonymous

I know but mathematics doesn't magically happen, you need to study a lot( and suffer lol) dont worry

- anonymous

if you do the same with the second triangle

- anonymous

sin 45 = sqrt 2 / 2

- anonymous

sqrt 2 / 2 = 21 / h

- anonymous

h = 29.698

- anonymous

now we calculate the cosinus

- anonymous

cos 45 = sqrt 2 / 2

- anonymous

sqrt 2 / 2 = x / 28,698

- anonymous

x = 20,292

- anonymous

distance from underneath the ballon to the second rope = 36, 373 + 20,292 = 56,665 feet

- anonymous

and it's solved

- Falco276

wait, but earlier you said that x is 36- never mind :P

- anonymous

that's the distance between underneath the balloon and rope 2

- Falco276

ah, i see.

- anonymous

and 20,292 ft is the distance between underneath the balloon and rope 1

- anonymous

sorry

- Falco276

got it.

- anonymous

36ft is the distance between rope 2 and 1

- anonymous

then you calculate from rope 1 to underneath the ballon and it gives you 20 ft

- anonymous

you add it and you obtain the final result

- Falco276

okay.

- 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

needed*

- anonymous

you did well! at least you had ideas! you only need to learn the theory well

- anonymous

i also think your teachers are crazy though

- 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

You are welcome, sure, see you! :D

- Falco276

thanks! (thumbs up)

- 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

oh, i understand, dont worry! my teachers are really nice.

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