Angle between lines

Calculate the angle between these two lines:

p:−4x+7y+7=0
q:−x+4y+7=0

Correct answer:

θ =  20.6 °

Step-by-step explanation:

n=(−4,7) m=(−1,4)  x1​=ny​nx​​=7(−4)​=−74​≐−0.5714 x2​=my​mx​​=4(−1)​=−41​=−0.25  θ1​=arctan(1−x1​⋅ x2​∣x1​−x2​∣​)=arctan(1−(−0.5714)⋅ (−0.25)∣(−0.5714)−(−0.25)∣​)≐0.3588 rad  θ=θ1​→  °=θ1​⋅ π180​   °=0.3588⋅ π180​   °=20.6  °=20.6∘=20°33′22"

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You need to know the following knowledge to solve this word math problem:

geometryarithmeticplanimetricsgoniometry and trigonometryUnits of physical quantitiesGrade of the word problem

 
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