SOLUTION: Find the length of the segment

Algebra ->  Coordinate-system -> SOLUTION: Find the length of the segment      Log On


   

Question 118095: Find the length of the segment
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given line segment

Photobucket


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


Photobucket

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

Photobucket


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)

Photobucket

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%5E2%2Bb%5E2=c%5E2 where a and b are the legs of the triangle and c is the hypotenuse



3%5E2%2B2%5E2=x%5E2 Plug in a=3, b=2, and c=x. Now lets solve for x


9+%2B+4+=++x++%5E+2 Square each individual term



1+3+=++x++%5E+2 Combine like terms


s+q+r+t+%28+1+3+%29+=+s+q+r+t+%28++x++%5E+2+%29 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