Answer:
0.0035 radians
0.2°
Step-by-step explanation:
If two non perpendicular lines have slopes m₁ and m₂, the angle between the two straight lines is,
tan θ [tex]= |\frac{m_{1} - m_{2}}{1 + m_{1}m_{2}} |[/tex]
θ = [tex]tan^{-1}|\frac{m_{1} - m_{2}}{1 + m_{1}m_{2}} |[/tex]
where
θ is angle between two straight lines
m₁ is the slope of the first straight line
m₂ is the slope of the second straight line
The first step is to calculate the slopes of the two straight lines.
Generally, the equation of a straight line is given by,
y = mx + c
where,
m is the slope or gradient
c is the y-intercept
Line 1 is given to be 4x - 4y = 4. Rearranging the equation we have
-4y = -4x + 4
y = x - 1 ........(1)
Comparing line equation (1) with general line equation for line 1, y = m₁x + c₁
m₁ = 1
Line 2 is given to be 5x + 4y = 6. Rearranging the equation, we have
4y = -5x + 6
[tex]y = \frac{-5}{4}x + \frac{6}{4}[/tex] ........(2)
Comparing line equation (2) with general line equation for line 2, y = m₂x + c₂
[tex]m_{2} = \frac{-5}{4}[/tex]
Now that we have both m₁ and m₂, we can substitute the values of m₁ and m₂ to calculate the angle between the two straight lines.
θ = [tex]tan^{-1}|\frac{1 - (-5/4)}{1 + (1)(-5/4)} |[/tex]
θ = [tex]tan^{-1}|\frac{1 + 5/4)}{1 - 5/4} |[/tex]
θ = [tex]tan^{-1}|\frac{9/4)}{-1/4} |[/tex]
θ = [tex]tan^{-1}|-9|[/tex]
θ = [tex]tan^{-1}9[/tex]
θ = 0.158°
θ = 0.2° (to 1 decimal place for degree)
Conversion from degrees to radians
Since 1° = π/ 180 radians
0.2° = 0.2 × π/ 180 radians
= 0.00349 radians
= 0.0035 radians (to 4 decimal places for radians)
The angle between two straight lines is 0.2° in degrees or 0.0035 radians
