Find the acute angle, in degrees, between the lines.
-$y = \sqrt { 3 } x + 16$ and $y = - \sqrt { 3 } x + 8$
A) $60 ^ { \circ }$
B) $45 ^ { \circ }$
C) $30 ^ { \circ }$
D) $75 ^ { \circ }$

Question

Quizplus · Accepted Answer

The slopes of the given lines are $m_1 = \sqrt{3}$ and $m_2 = -\sqrt{3}$, respectively. The formula to find the angle $\theta$ between two lines with slopes $m_1$ and $m_2$ is $\tan(\theta) = \left| \frac{m_1 - m_2}{1 + m_1m_2} \right|$. Substituting $m_1 = \sqrt{3}$ and $m_2 = -\sqrt{3}$ gives $\tan(\theta) = \left| \frac{\sqrt{3} - (-\sqrt{3})}{1 + (\sqrt{3})(-\sqrt{3})} \right| = \left| \frac{2\sqrt{3}}{1 - 3} \right| = \sqrt{3}$, which corresponds to a $60^\circ$ angle.

Find the Acute Angle, in Degrees, Between the Lines y=3x+16y = \sqrt { 3 } x + 16y=3​x+16

Find the Acute Angle, in Degrees, Between the Lines $y = \sqrt { 3 } x + 16$