Question

What is the acute angle between the lines y = 3x + 2 and y = 4x + 9?

• A. 4.4${}^{\circ }$
• B. 28.3${}^{\circ }$
• C. 5.2${}^{\circ }$
• D. 18.6${}^{\circ }$
• E. none of these

Answer 1

Answer: (A)

4.4${}^{\circ }$

$y=3x+2$

$m_1=3$

$=>tan{\theta }_1=3$

$=>{\theta }_1=ta{n}^{-1}\left(3\right)$

$=>{\theta }_1={71.57}^0$

Again,

$y=4x+9$

$=>m_2=4$

$=>tan{\theta }_2=4$

$=>{\theta }_2=ta{n}^1\left(4\right)$

$=>{\theta }_2={75.96}^0$

$\therefore$ Angle between the lines

$={\theta }_2-{\theta }_1$

$=75.96-71.56$

$={4.4}^0$