Calculate, correct to one decimal place, the acute angle between the lines 3x – 4y + 5 = 0 and 2x + 3y – 1 = 0.
-
A.
70.6° -
B.
50.2° -
C.
39.8° -
D.
19.4°
Correct Answer: Option A
Explanation
(tan theta = frac{m_{1} – m_{2}}{1 – m_{1}m_{2}})
(m_{1} = text{slope of 1st line } 4y = 3x + 5 implies y = frac{3}{4}x + frac{5}{4})
(m_{1} = frac{3}{4})
(m_{2} = text{slope of 2nd line} 3y = 1 – 2x implies y = frac{1}{3} – frac{2}{3}x)
(m_{2} = -frac{2}{3})
(tan theta = frac{frac{3}{4} – (-frac{2}{3})}{1 – ((frac{3}{4})(-frac{2}{3}))} = frac{frac{17}{12}}{frac{1}{2}})
(tan theta = frac{17}{6})
(theta approxeq 70.6°)