I have a triangle problem that I am in desperate need of help with with. Here is what I know ...
the triangle is mapped on a graph where I only know y-axis coordinates for 2 points, the length of one side, and a percentage of a second side as per details below:
the 3 y-axis point coordinates (A,B,C) Ay=2.23, By=3.39, Cy=???
the 3 x-axis point coordinates of Ax, Bx, Cx are all unknown
the length of the side A to B is 1.16
the length of the side B to C=261.8% of the length of A to C
don't know any angles
I need to determine ...
the value of coordinate of Cy and/or the length of the side from A to C or alternatively, the length of the side from B to C Can anyone help? Thank you in advance.
Draw a diagram in the plane, with the constant lines $\;y=2.23\;,\;y=3.39\;$ (note that the distance between these two lines is precisely $\;1.16\;$ ...!) .
On these lines the point $\;A,B\;$ are located. Now, taking into account the length $\;AB\;$ we get the points $\;A,B\;$ are on thesame vertical line, so we can already determine that
$$A=(x_0\,,\,2.23)\;\;,\;\;B=(x_0\,,\,3.39)\;\;(\text{same abscissa}\;\;x_0\;\;\text{for both points !})$$
Since we're given $\;BC=2.2618\cdot AC$ , it's clear point $\;C\; $ "is on the side of point$\;A\;$ " , but this is a rather blurry notion.
But there's no way to determine the coordinate of $\;C\;$ as it could be on the right side of the line $\;x=x_0\;$ or on its left, so the lengths $\;AC\;,\;BC\;$ cannot be known