Rocket math question, in urgent need of help?

Question

A test rocket follows a parabolic path. Its path is followed by two tracking stations. A & B. On a grid system, the launch pad is at (0,0). The tracking stations are on the horizontal axis. Station A is 4.5 KM from the launch site and station B is 7 km from the launch site.

The tracking stations record two measurements: the first, station A records an angle of 78.2 degrees and station B records an angle of 67.4 degrees, the second places the rocket at the co-ordinates (10,20) on the parabola.

***Find the EQUATION of the flight path. Find how FAR from the launch site the rocket lands***

I need ALL the steps to finding this answer, I need it for tomorrow!!!

Answer 1

assume the two stations are on one side of the launch pad

the equation that presents its path will be in the form of:
y = ax^2 + bx + c

but to find that equation, we must first use:
y = .5at^2 + Vt + Xi

let A be the position where the rocket is lauch.
Let B be the position where the rocket is tracked by the two stations.
Let C be where the station A is at
Let D be where the station B is at

From there, you should be able to draw a big triangle consist of two smaller triangle ABC and ABD.

Now draw an altitude from B to opposite side. Let's call E is a point where the altitude bisect the opposite side

From the given informations:
AC = 4.5km
AD = 7km

Let x be the length of AE, then 4.5 - x is the length of EC
and 7- x is the lenth of ED

lets call the altitude h

tan(78.2) = h/(4.5 - x)
tan(67.4) = h/(7 - x)

h = tan(78.2)(4.5 - x)
h = tan(67.4)(7 - x)


tan(78.2)(4.5 - x) = tan(67.4)(7 - x)
tan(78.2)4.5 - tan(78.2)x = tan(67.4)7 - tan(67.4)x
tan(78.2)4.5 - tan(67.4)7 = -tan(67.4)x+ tan(78.2)x
tan(78.2)4.5 - tan(67.4)7 = x (-tan(67.4)+ tan(78.2) )
x =( tan(78.2)4.5 - tan(67.4)7 ) / (-tan(67.4)+ tan(78.2) )
x = 1.9811

h = tan(78.2)(4.5 - x)
h = tan(78.2)(4.5 - 1.9811)
h = 12.0569km

So when the rocket is recorded, its altitude is 12.0569km

I can't go any further because there isn't enough information to find the origional speed other rocket. We need speed to plug in the equation y = .5at^2 + Vi +yi

Answer 2

I think you should have copied and pasted the original question here. What we don't know is
# does (x,y)=(10,20) means when x=10km y=20km?
This conflicts with your statement that station B is 7km not 10km when the measurement was made. Does it mean that the measurements were made not directly overhead of stations A or B?
# If the measurements were not made directly overhead A or B, were they made simultaneously?

What I can guess is the question is an exercise of the geometric definition of a parabola,
A parabola is generated as the tangential locus of a line of constant length connecting the opposite points of another two lines placed at an angle of each other.
Resulting in an equi-ratio at any point of the parabola which is too difficult to describe without a drawing.

Answer 3

There is not enough information. Which SIDE of the launch pad are the two tracking stations on? Also, which side of the current location of the rocket are they on?