To find the angle between two lines, we need to find the slope of each line and then use the formula:
θ = | arctan((m2 - m1) / (1 + m1m2)) |
where m1 and m2 are the slopes of the two lines.
First, let's rearrange each equation to the slope-intercept form y = mx + b:
3x - 2y = 0 -> y = (3/2)x
x + 3y + 4 = 0 -> y = (-1/3)x - 4/3
The slopes of the two lines are m1 = 3/2 and m2 = -1/3.
Plugging these values into the formula, we get:
θ = | arctan((-1/3 - 3/2) / (1 + (3/2)(-1/3))) |
θ = | arctan(-7/3) |
Using a calculator, we find that the angle is approximately 109.5 degrees, which is closer to 90 degrees than any of the given answer choices. Therefore, the correct answer is (d) 90.