Mathematics

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


ANSWER

4.4$$\displaystyle ^{\circ}$$


SOLUTION
$$y=3x+2$$
$$m_1=3$$
$$=>tan\theta_1=3$$
$$=>\theta_1=tan^{-1}(3)$$
$$=>\theta_1=71.57^{0}$$
Again,
$$y=4x+9$$
$$=>m_2=4$$
$$=>tan\theta_2=4$$
$$=>\theta_2=tan^{1}(4)$$
$$=>\theta_2=75.96^{0}$$
$$\therefore$$ Angle between the lines
$$=\theta_2-\theta_1$$
$$=75.96-71.56$$
$$=4.4^{0}$$
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