Finding the Degree of of triangle.

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To determine the launch angle of a water balloon using the provided quadratic equations for X and Y values over time, the user initially assumed that the lengths corresponding to these equations could indicate a 45-degree angle if they were equal. However, upon calculating, the user found that the X value (55.81) and Y value (52.62) are not equal, suggesting the angle is not 45 degrees. The discussion includes confusion about the application of the sine function, the relevance of converting values to percentages, and the need for clarity on how to derive the triangle's sides from the quadratic equations. Ultimately, the user seeks guidance on calculating the launch angle based on the coordinates of the water balloon's launch.
anto3232
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Homework Statement


I have to find the degree at which I am launching a water balloon and i have 2 quadratic formulas for the X and Y values versus time. The X and Y quadratic formulas for it was, X: 55.81t^2+(-2.197t)+0.5222
Y:52.62t^2+(-2.358t)+.4135


Homework Equations


Is A the length of x or y, and for 45 degrees shouldn't it be equal? for it to equal 45 degrees?


The Attempt at a Solution


Well i used a^2+b^2=C^2 and got 76.70, then i figured the angle of that side was 90 degrees so i set Sin (90)/76.70=sin (b)/52.62
and got .61 so i converted to % which is 61% but looking at the graph it didnt make much sense seeing as the length of A is greater than the Heigh (b) so wouldn't angle B, be smaller ?
 
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anto3232 said:

Homework Statement


I have to find the degree at which I am launching a water balloon and i have 2 quadratic formulas for the X and Y values versus time. The X and Y quadratic formulas for it was, X: 55.81t^2+(-2.197t)+0.5222
Y:52.62t^2+(-2.358t)+.4135


Homework Equations


Is A the length of x or y, and for 45 degrees shouldn't it be equal? for it to equal 45 degrees?
This space is for relevant equations, not questions. Anyway, how do you know that the balloon was launched at an angle of 45 degrees?
anto3232 said:

The Attempt at a Solution


Well i used a^2+b^2=C^2 and got 76.70,
For what, c? And what did you use for a and b?
anto3232 said:
then i figured the angle of that side was 90 degrees so i set Sin (90)/76.70=sin (b)/52.62
and got .61
For what? Help us out here. Is this sin(b)?
anto3232 said:
so i converted to %
Why did you do that? I have no idea why you'd want to convert to a percent.
anto3232 said:
which is 61% but looking at the graph it didnt make much sense seeing as the length of A is greater than the Heigh (b) so wouldn't angle B, be smaller ?

You need to show us how you got sides a and b of your triangle.
 
Mark44 said:
This space is for relevant equations, not questions. Anyway, how do you know that the balloon was launched at an angle of 45 degrees?
Thats what I am trying to figure out, I am pretty sure it didnt because for my y graph i got 52.62 and for the x graph i got 55.81 which isn't equal meaning it aint 45 Degrees, so what I am trying to say is since i know the a and b how do i figure out the angle?
For what, c? And what did you use for a and b?
a=the x which is 55.81 and b= the y which is 52.62.
For what? Help us out here. Is this sin(b)?

Why did you do that? I have no idea why you'd want to convert to a percent.


You need to show us how you got sides a and b of your triangle.
Well i thought A for some reason was the 55.81 and B was the 52.62 from the two quadratic formulas, but i think that isn't right...

Hmm hold on ill let me take a look at what I am doing
 
okay so i have a water balloon launcher, it starts off at 0.51410733857,0.404340993843
and at the end of the launch its at 1.2249085093,1.03940105622, this is in meters btw..
What i need to do is find the angle or degree it launch's at. Do i X2-X1/Y2-Y1 it? I don't know that would just give me the slope but could that help me get the angle?
 
What's the exact wording of the problem? It seems like the problem as you first described it is different from what you have now. Where did the quadratic equations come from?
 
I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
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