# Find the length of the the green line

How can you find the length of the green line? The blue lines have a length of 8. Right angles are marked.

(Diagram not to scale)

EDIT: Here's a second diagram (The green lines are not the same length just focus on the bottom and the yellow-purple angle is 90 degrees):

Diagram not to scale

EDIT2: The relative sizes are:

For the red-brown triangle sides: Red 1.0, bottom brown 1.59149, right brown 1.23808

For the green-blue-brown triangle: Green 1.0, top blue with right brown 1.59149, bottom blue-brown 1.23808

EDIT3: The problem I'm trying to solve is "what should the length of the green and orange lines (from the diagram below) be in order for the blue lines to be equal?":

3rd diagram

• Did you try to construct it? Unless length of brown lines is also given, the length of green lines cannot be determined. Jan 28 '20 at 15:23
• @Narasimham I'm trying to figure out the lengths of the brown lines which should depend on the angles. They are extensions of the blue lines. Jan 28 '20 at 15:26
• Is the bottom blue line also supposed to be of length 8? In that case the general shape of your diagram is off, the bottom blue line would intersect the red line at a point above the bottom corner of the square, not below it. Jan 28 '20 at 15:31
• @quarague The diagram doesn't represent the true lengths. The bottom blue line is the top of the black lines. The red line starts from the right black line. Jan 28 '20 at 15:34

The given information is not enough to find the length of the green line.

If we make the assunption that those right triangles are congruent to each other then we may approach as follows.

Using the length of the blue segment and the measure of the angle opposite to that we figure out that the length of the green line is $$8 \tan (38.928) = 6.4616..$$

It is not possible to determine length of green line segment without an idea about brown line segment lengths.

This is clear by rotating rectangle about a point where the green and yellow lines meet. Lengths of brown line segments are seen to vary with such a rotation.

For example if slant brown line segment is 3 units then green line length is

$$11 \cos 51.072^{\circ}=6.911773$$