What we need to do is to see the angle x and find other angles which are also x and then locate right angled triangles containing x and finally use trigonometry to find the sides of the right angled triangles and thus the coordinates of the vertices of the square.
1. find angles equal to x
2. find right angled triangles with x
3. use aCosx and aSinx
Remember that the corners of the square are 90 degrees.
We have taken the sides of the large squares as p which is acutally equal to a^2+b^2
In the second diagram, we have two lines of the triangle for which we have found the equations.
We have used a trigonometric formula that says
Sin (180-x)=Sin x
Cos (180-x)= – Cos x
tan (180-x)= – tan x
and we have used the theorem for finding the equation of a line passing through (p,q) with slope, m is y – q = m (x – p)
We then turn the equilateral triangle by angle x in the clockwise direction like we had done for the square in an earlier example.
There is a mistake in the diagram. Can you spot it?
Hint: it is in the coordinates of V
See the answer below
We have also used advanced formulae for Sin (A+B) & Cos (A+B)
The x coordinate of V will be [a + pCosy], not pCosy as shown.