Question

find the Angle between the lines x+3y-8 and 2x-3y+6 =0

Answer 1

Answer:

52.001°

Step-by-step explanation:

Equation 1: x + 3y - 8 = 0

⇒ 3y = -x + 8

⇒ y = -x / 3 + 8/3

This is of the form, y = mx + c

Hence according to the formula we get,

⇒ m₁ = -1/3 and intercept = 8/3

Similarly Equation 2: 2x - 3y + 6 = 0

⇒ 3y = 2x + 6

⇒ y = 2x/3 + 6/3

⇒ y = 2x/3 + 2

⇒ m₂ = 2/3 and intercept = 2

We know that Tan of angle between lines  can be calculated as:

Tan A = | m₁ - m₂ | / 1 + m₁m₂

⇒  Tan A =  | -1/3 - 2/3 | / 1 + ( -1/3)(2/3)

⇒ Tan A = | -3/3 | / 1 - 2/9

⇒ Tan A = | -1 | / 9 - 2 / 9

⇒ Tan A = 1 / 7/9

⇒ Tan A = 9/7 = 1.28

⇒  A = Tan ⁻¹ ( 1.28 ) = 52.001°

Hence the angle between the two lines is 52.001°

Thanks !!