SOLUTION: find the acute angle between the lines: 4x+3y-1=0 and 2x-5y-11=0 (1dp) after finding the angle of inclination of each line, then what do i do?

Algebra ->  Expressions-with-variables -> SOLUTION: find the acute angle between the lines: 4x+3y-1=0 and 2x-5y-11=0 (1dp) after finding the angle of inclination of each line, then what do i do?      Log On


   

Question 1049462: find the acute angle between the lines:
4x+3y-1=0 and 2x-5y-11=0 (1dp)
after finding the angle of inclination of each line, then what do i do?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(1) +4x+%2B+3y+-+1+=+0+
(2) +2x+-+5y+-+11+=+0+
-----------------------
(1) +3y+=+-4x+%2B+1+
(1) +y+=+-%284%2F3%29%2Ax+%2B+1%2F3+
and
(2) +5y+=+2x+-+11+
(2) +y+=+%282%2F5%29%2Ax+-+11%2F5+
-----------------------------
For (2), think of a unit vector in the 1st
quadrant with an angle +a+ that has
+tan%28a%29+=+2%2F5+
+a+=+arctan%28+.4+%29+
+a+=+21.8014+ degrees
------------------------------
Think of (1) as a unit vector in the 4th quadrant
with +tan%28b%29+=+-4%2F3+%29+
+b+=+arctan%28+-4%2F3%29+
+b+=+-53.1301+
------------------------
The angle between the lines is:
+a+-+b+=+21.8014+%2B+53.1301+
+a+-+b+=+74.9315+ degrees is
the acute angle between the lines
---------------------------------
Here's the plot of lines:

My answer looks possible