Answer:
The angle between the two lines is 72.35° ⇒ to the nearest hundredth
Step-by-step explanation:
- The angle between the two lines is the difference between their angles with the positive part of the x-axis (Ф = Ф - Ф)
- The slope of the line equal to the tangent of the angle between the line and the positive part of the x-axis (m = tan Ф)
- The slope of the line whose equation is ax + by = c is m =
∵ The equation of the first line is 4x - 5y = 11
∴ a = 4 and b = -5
→ By using the 3rd rule of the slope above
∵ m = =
∴ m = 0.8
→ By using the 2nd rule above
∵ tan Ф = 0.8
∴ Ф = (0.8)
∴ Ф = 38.66° ⇒ to the nearest hundredth
∵ The equation of the first line is 2x + 3y = 7
∴ a = 2 and b = 3
→ By using the 3rd rule of the slope above
∵ m =
∴ m =
→ By using the 2nd rule above
∵ tan Ф =
∴ Ф = ( )
∴ Ф = -33.69° ⇒ to the nearest hundredth
→ By using the 1st rule above
∵ Ф = -33.69 - 38.66
∴ Ф = -72.35°
→ Ignore the negative sign
∴ The angle between the two lines is 72.35° ⇒ to the nearest hundredth
<u><em>V.I.N:</em></u>
<em>You can use this rule to find the angle between 2 lines</em> tan Ф = II