Question 567630
What is the angle between the horizontal (x) axis and the line containing the points (2,8) and (4,9)? 
<pre>
{{{drawing(800,1600/3,-15,6,-3,11, graph(800,1600/3,-15,6,-3,11), 
circle(2,8,.1), locate(2,8,"(2,8)"), circle(4,9,.1), locate(4,9,"(4,9)"),
green(line(14,14,-18,-2)),locate(-12,.7,theta), red(triangle(2,8,4,9,4,8)),
red(arc(-14,0,7,-7,0,26.56505118)),locate(2.7,8.4,theta),
red(arc(2,8,2.5,-2.5,0,26.56505118))  


)}}}

We observe that the angle <font face="symbol">q</font> that the green line makes with the 
x-axis is the same size angle as the angle marked <font face="symbol">q</font> in the little right
triangle up where the two given points are.

In that little right triangle we see that the opposite side of <font face="symbol">q</font> is 
1 unit long and the adjacent side to <font face="symbol">q</font> is 2 units long, 
so we use the trig function that involves opposite and adjacent:

                 tan(<font face="symbol">q</font>) = {{{opposite/(adjacent)}}}
                 tan(<font face="symbol">q</font>) =   {{{1/2}}}

Use the inverse tangent fuction on the calculator and get

                 <font face="symbol">q</font> = 26.56505118° = 26°33'54"

I hope you observed that the tangent of that angle <font face="symbol">q</font> is the slope
of the green line.
                                                      
Edwin</pre>