find the sine of the angle

Question

formed by two rays that start at the origin of the Cartesian plane if one ray passes through the point (3sqr3,3) and the other ray passes through the point (-4,4sqr3).

 

how do i get an answer of 1?

Answer 1

Say, the angle formed by the first line on y axis=a1

 

       the angle formed by the second line on y axis =a2

 

You can draw the figure to better understand

 

Sin(a1)=3sqrt(3)/6

 

           sqrt(3)/2

a1=60 dig

 

Sin (a2)=4sqrt(3)/8

 

           = sqrt(3)/2

 

     a2=60 deg

 

a1+a2=120 dig

 

sin(120)=sqrt(3)/2