Answer:
70.6°
Step-by-step explanation:
The angle between the 2 lines can be calculated using
tanΘ = | [tex]\frac{m_{2}-m_{1} }{1+m_{1}m_{2} }[/tex] | ( Θ is the angle between the lines )
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Rearrange the 2 equations into this form to extract the slopes
3x - 4y + 5 = 0 ( subtract 3x + 5 from both sides )
- 4y = - 3x - 5 ( divide all terms by - 4 )
y = [tex]\frac{3}{4}[/tex] x + [tex]\frac{5}{4}[/tex] with m = [tex]\frac{3}{4}[/tex] ← [tex]m_{2}[/tex]
--------------------------------------------
2x + 3y - 1 = 0 ( subtract 2x - 1 from both sides )
3y = - 2x + 1 ( divide all terms by 3 )
y = - [tex]\frac{2}{3}[/tex] x + [tex]\frac{1}{3}[/tex] with m = - [tex]\frac{2}{3}[/tex] ← [tex]m_{1}[/tex]
Note it does not matter which slope is labelled [tex]m_{1}[/tex] or [tex]m_{2}[/tex]
Thus
tan Θ = | [tex]\frac{\frac{3}{4}+\frac{2}{3} }{1+(-\frac{2}{3})\frac{3}{4} }[/tex]
= | [tex]\frac{\frac{17}{12} }{\frac{1}{2} }[/tex] = | [tex]\frac{17}{6}[/tex] | = [tex]\frac{17}{6}[/tex] , then
Θ = [tex]tan^{-1}[/tex] ([tex]\frac{17}{6}[/tex] ) ≈ 70.6° ( to 1 dec. place )
