Saturday, July 4, 2009

`0.05x - 0.03y = 0.21, 0.07x + 0.02y = 0.16` Find the angle theta (in radians and degrees) between the lines

Given 


`0.05x-0.03y=0.21`


`0.07x+0.02y=0.16`



Find the slope for line 1.


`0.05x-0.03y=0.21`


` ` `5x-3y=21`


`-3y=-5x+21`


`y=5/3x-7`


The slope of line 1 is 5/3.



Find the slope of line 2.


`0.07x+0.02y=0.16`


`7x+2y=16`


`2y=-7x+16`


`y=-7/2x+8`


The slope for line 2 is -7/2.



Find the angle between the two lines by using the formula


`tan(theta)=|(m_2-m_1)/(1+m_1m_2)|`


`tan(theta)=|[(-7/2)-(5/3)]/[1+(5/3)(-7/2)]|`


`tan(theta)=(-31/6)/(-29/6)=31/29`


`theta=arctan(31/29)=46.9^@=0.8187`  radians.



The angle between the given lines is 46.9 degrees or 0.8187 radians.

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