Question 118095
Start with the given line segment


<a href="http://s150.photobucket.com/albums/s91/jim_thompson5910/?action=view&current=drawing.png" target="_blank"><img src="http://i150.photobucket.com/albums/s91/jim_thompson5910/drawing.png" border="0" alt="Photobucket"></a>



Draw a line straight down from the right end of the line segment



<a href="http://s150.photobucket.com/albums/s91/jim_thompson5910/?action=view&current=step1-1.png" target="_blank"><img src="http://i150.photobucket.com/albums/s91/jim_thompson5910/step1-1.png" border="0" alt="Photobucket"></a>


From that point, draw a horizontal line to the left end of the line segment. Notice how a right triangle is formed.


<a href="http://s150.photobucket.com/albums/s91/jim_thompson5910/?action=view&current=step2-1.png" target="_blank"><img src="http://i150.photobucket.com/albums/s91/jim_thompson5910/step2-1.png" border="0" alt="Photobucket"></a>



From the picture, we can see that the triangle has legs of 2 and 3 and an unknown hypotenuse (which is the length of the line segment)


<a href="http://s150.photobucket.com/albums/s91/jim_thompson5910/?action=view&current=finalstep1.png" target="_blank"><img src="http://i150.photobucket.com/albums/s91/jim_thompson5910/finalstep1.png" border="0" alt="Photobucket"></a>


Since we can see that the triangle has legs of 3 and 2 with a hypotenuse of x, we can use Pythagoreans theorem to find the unknown side.



Pythagoreans theorem:


{{{a^2+b^2=c^2}}} where a and b are the legs of the triangle and c is the hypotenuse




{{{3^2+2^2=x^2}}}  Plug in a=3, b=2, and c=x. Now lets solve for x



{{{9 + 4 =  x  ^ 2}}} Square each individual term




{{{1 3 =  x  ^ 2}}} Combine like terms



{{{s q r t ( 1 3 ) = s q r t (  x  ^ 2 )}}} Take the square root of both sides



Which approximates to...


{{{3.60555127546399=x}}}


So our answer to the nearest hundredth is 

{{{x=3.61}}}


So the line segment is about 3.61 units long