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 2 years ago
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.
 2 years ago
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.

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Falco276
 2 years ago
Best ResponseYou've already chosen the best response.1If 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
 2 years ago
Best ResponseYou've already chosen the best response.1I think I know. The vertical angle measurement is equal to the horizontal measurement of the right angle.

Falco276
 2 years ago
Best ResponseYou've already chosen the best response.121 feet by 21 feet. I just have to find out the measurement to rope 2

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1they are asking you the distance between rope 2 and underneath the balloon right?

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1just to make sure i understood well, i remind you i'm not english!! hehehe

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1lemme get a paper so i can explain better

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1the distance between rope 2 and 1 is x right? as the drawing says

Falco276
 2 years ago
Best ResponseYou've already chosen the best response.1yes, but I found the half of X which is 45.

Falco276
 2 years ago
Best ResponseYou've already chosen the best response.1look at the drawing, am I right?

Falco276
 2 years ago
Best ResponseYou've already chosen the best response.1I only have to fing the measurement that is the question mark.

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1you have 2 angles if you notice

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1even though they dont give you a number, you can see that the angle underneath the balloon is 90, a right triangle

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1ah well you need to find the sides first, nevermind

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1you gonna solve the problem like this

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1x: distance from rope 2 to underneath the balloon  distance from rope 1 to underneath the balloon

Falco276
 2 years ago
Best ResponseYou've already chosen the best response.1distance from rope 1 to underneath the balloon = 45.

Falco276
 2 years ago
Best ResponseYou've already chosen the best response.1Im trying to figure out rope 2

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1how do you know its 45? 45 is the given angle

Falco276
 2 years ago
Best ResponseYou've already chosen the best response.1no, 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.

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1it has a lot to do with sinus and cosinus

Falco276
 2 years ago
Best ResponseYou've already chosen the best response.1its 21!!!!!! Its 21!!!!

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1well first you need to remember that sinus = op side / h

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1we are measuring from rope 1 to balloon now, so sin 30 right?

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1i tell you that sin 30 = 1/2

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1so you gonna put 1/2 = 21ft / h right?

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1solve for h and then you have the hypotenuse

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1what do you think you can do next

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1there are many ways to solve this problem

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1also remember that all the angles of a triangle = 180, if this doesn't happen, it's not a triangle

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1so if you have a 90º angle, a 30º angle...what's the other angle?

Falco276
 2 years ago
Best ResponseYou've already chosen the best response.1wait, so were trying to find a measurement form rope 1 to the balloon, am I right?

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1i got it already, just waiting to see how you proceed

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1that 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
 2 years ago
Best ResponseYou've already chosen the best response.1I never took trigonometery before.

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1I know you haven't heard of the trigonometric functions

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1you need to do it 2 steps

Falco276
 2 years ago
Best ResponseYou've already chosen the best response.1no, never. I just take basic geometry.

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1do you remember what was the sinus and what was the cosinus?

Falco276
 2 years ago
Best ResponseYou've already chosen the best response.1(sigh) I don't remember. (honest, i don't want to be mean to you.)

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1hahaha, 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
 2 years ago
Best ResponseYou've already chosen the best response.1okay, I'll take your note.

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1Now you need to MEMORIZE this scheme, mathematics are also a subject to study!

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1now ill draw you a triangle and you'll tell me which is the oppsite and which is the adjacent side ok?

Falco276
 2 years ago
Best ResponseYou've already chosen the best response.1I think the opposite side is left from angle A the adj side is right from Angle A.

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1opposite = infront of the angle

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1adjacent = sidewards the angle

Falco276
 2 years ago
Best ResponseYou've already chosen the best response.1fine! Isn't the adjecent side the How do I Explain it! Isnt the adjecent side the sidewards of the angle?

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1no, the other one, that's the hypotenuse

hba
 2 years ago
Best ResponseYou've already chosen the best response.0@GCR92 is helping you,Just follow him :)

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1I have to explain the whole trigonometry before you are able to solve that problem...

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1I explain as simple as it is, but not simpler

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1we are going to solve 2 triangles

Falco276
 2 years ago
Best ResponseYou've already chosen the best response.1wait. I think I have it.

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1we 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

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1and we can make a relationship

Falco276
 2 years ago
Best ResponseYou've already chosen the best response.1tan 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
 2 years ago
Best ResponseYou've already chosen the best response.1oh, no i meant 21 (facepalm)

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1You could've done it if you had the value of the x side

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1but that's what we are looking for

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1to use the tangent you need to have the value of 2 sides

Falco276
 2 years ago
Best ResponseYou've already chosen the best response.1now we take the other triangle.

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1the adjacent side is not 21, 21 is the only data they give us, you can't invent it

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1listen 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

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1sin 30 = 1/2, we do that in order to calculate H

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1now we take the cosinus in order to calculate X

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1you can never write tan and let it alone

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1it is always tan OF SOMETHING

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1tan of x, tan of alfa, tan of 20

Falco276
 2 years ago
Best ResponseYou've already chosen the best response.1so the answer is 21 sq. root 3

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1take the 30º triangle and then, sin 30 = 1/2

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1now we have the h of the first triangle

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1now we can calculate the distance from the rope to underneath the balloon, that distance will be given by the cosinus

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1now we go to the second triangle and apply exactly the same steps but with 45º

Falco276
 2 years ago
Best ResponseYou've already chosen the best response.1maybe my way of solving this problem was wrong. sorry.

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1I know but mathematics doesn't magically happen, you need to study a lot( and suffer lol) dont worry

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1if you do the same with the second triangle

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1now we calculate the cosinus

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1distance from underneath the ballon to the second rope = 36, 373 + 20,292 = 56,665 feet

Falco276
 2 years ago
Best ResponseYou've already chosen the best response.1wait, but earlier you said that x is 36 never mind :P

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1that's the distance between underneath the balloon and rope 2

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1and 20,292 ft is the distance between underneath the balloon and rope 1

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.136ft is the distance between rope 2 and 1

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1then you calculate from rope 1 to underneath the ballon and it gives you 20 ft

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1you add it and you obtain the final result

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1what 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!

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1you did well! at least you had ideas! you only need to learn the theory well

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1i also think your teachers are crazy though

Falco276
 2 years ago
Best ResponseYou've already chosen the best response.1XD 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.

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1You are welcome, sure, see you! :D

GCR92
 2 years ago
Best ResponseYou've already chosen the best response.1I 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
 2 years ago
Best ResponseYou've already chosen the best response.1oh, i understand, dont worry! my teachers are really nice.
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