Question

Find the acute angle between 3x - 2y + 7 = 0 and 2y + 4x - 3 = 0 to the nearest degree.

Answer 1

Answer:

≈ 60°

Step-by-step explanation:

tan (β - α) = (tanβ - tanα) / (1 + tanα×tanβ)

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3x - 2y = - 7 ⇒ y = (3/2)x + 7/2 ⇒ m = 3/2 = tanα

4x + 2y = 3 ⇒ y = - 2x + 3/2 ⇒ m = - 2 = tanβ

tan (β - α) = (- 2 - 3/2) ÷ (1 + (- 2)(3/2))

tan (β - α) = (- 3.5) ÷ (- 2) = 1.75

x = β - α ≈ 60°