Find the Area of a Rectangular Plane with 3 Sequential Tips

[vabamyyr]

i started to work on a problem. A point on a plane is away from 3 sequential tips
of rectangular respectively 3, 4, 5 units. Find the area of rectangular. I have an image.

 

[robphy]

Did you mix up alpha and beta? (check the angles in the equations)

 

[vabamyyr]

on the image alfa and beta were mixed up but corrected now

 

[boteet]

Hello, I am linguist teacher, I am sorry for posting in your thread, because I really don't know how to start a thread, I have got a problem in math class, i take it as my second degree, very basic but i don't know how to solve it
I have a big square with one point(x,y) inside it, i have tow other small rectangles, with a given width (B), the two rectangles are drawn, divided with lines, into very small squares, then I put one head of one rectanguler into the square at one edge of the square, and the other rectangler is done the same but from the opposite edge, such that the point is on the line from rectanguler to other rectaguler.
But not all rectangler width is inside the square. If i know how many the very small squares in the 2 rectagulers are inside the big square, How can i find the centroid of the big square ?
Thanks a bunch

 

[boteet]

can someone help me please ?

 

[rachmaninoff]

i started to work on a problem. A point on a plane is away from 3 sequential tips...

To find the area, it would be enough to find the lengths of DC and CB, wouldn't it?

You're familiar with the theorem of cosines:

You know EC, EB, and α - can you find CB?
You know @, #, and (α + β) - can you find DC?

alfa and beta

Neat spelling of α - is that Estonian?

 

[vabamyyr]

i don`t know alfa

 

[rachmaninoff]

If you don't know the angles, then the area is not uniquely specified. This is clear if you try to shift point E downwards, while preserving the three known lengths - both the rectangle's sides increase, and so the area increases. Thus the area would not be uniquely specified.

 

[vabamyyr]

u have a rectangle and u can find a point which satisfies this condition. I wouldn`t say that the area isn`t uniquely specified otherwise why would this task be in a book. And answer should be 12

 

[rachmaninoff]

A clear example:
(ED=3, EC=4, EB=5)

D----E------C

A------------B

Area of ADCB: 7*3= 21

compare to:

E

D------------C
A----------- B

Area of ADCB: roughly 3.29...


Thus, ED, EC, and EB do not uniquely specify an area for ADCB; you need alfa and beta also.

 

[vabamyyr]

any other ideas, i hate to think that this task cannot be done

 

[rachmaninoff]

It's not the answer you're looking for;

Area = (DC) * (CB)
$$=\left( 3^2+4^2-2 \cdot 3 \cdot 4 \cdot \cos (\alpha + \beta) \right) \left( 4^2+5^2-2 \cdot 4 \cdot 5 \cdot \cos (\alpha) \right)$$
=...

As you see, it's dependent on both "alfa" and beta.