Find the angle (in radians and degrees) between the lines.Round your answer to four decimal places for radians and round your answer to one decimal places for degree.
A)

Question

Find the angle  (in radians and degrees) between the lines.Round your answer to four decimal places for radians and round your answer to one decimal places for degree. ​  ​
A)​

Quizplus · Accepted Answer

To find the angle between two lines, we need to find the angle formed by the vectors pointing in the direction of those lines. Using the slope-intercept form of two given lines, we can write them as: y = (-2/3)x + 4 and y = (-1/4)x + 3 To obtain the direction vectors of the lines, we take any two points on each line and find the vector between them. For the first line, we can take (-3,6) and (3,2): <3-(-3), 2-6> = <6,-4> So the direction vector for the first line is <6,-4>. Similarly, for the second line, we can take (0,3) and (4,2): <4-0, 2-3> = <4,-1> So the direction vector for the second line is <4,-1>. Using the dot product formula, we can find the angle between these vectors: cos(theta) = (6)(4) + (-4)(-1) / sqrt(6^2 + (-4)^2) * sqrt(4^2 + (-1)^2) = 26 / 29.68 ≈ 0.876 theta ≈ 29.56 degrees (rounded to one decimal place) To convert to radians, we multiply by pi/180: theta ≈ 0.5164 radians (rounded to four decimal places) Therefore, the answer is (C).

Find the Angle (In Radians and Degrees) Between the Lines.Round