`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.

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.