The biggest angle

[kate]

We have the points with coordinates [tex]A(0;4)[/tex] and [tex]B(3;8)[/tex].

Find the coordinates of point [tex]C[/tex] from the line [tex]y = 0[/tex], for which the angle [tex]\angle ACB[/tex] is maximal.

[Guest]

Let point c be (c, 0). The slope of line AC is [tex]\frac{4- 0}{0- c}= \frac{4}{c}[/tex]. The slope of line BC is [tex]\frac{8- 0}{3- c}= \frac{8}{3- c}[/tex]. Finally the angle between two lines with slopes m and n is given by [tex]tan(\theta)= \left|\frac{m- n}{1+ mn}\right|[/tex].