Find the acute angle that is formed by the line $y - \sqrt { 3 } x + 1 = 0$ and the x-axis
A) $60 ^ { \circ }$
B) $45 ^ { \circ }$
C) $30 ^ { \circ }$
D) $88 ^ { \circ }$
E) $24 ^ { \circ }$

Question

Quizplus · Accepted Answer

The slope of the line is given by the coefficient of $x$, which is $-\sqrt{3}$. The tangent of the angle that a line makes with the positive direction of the x-axis is equal to the slope of the line. Therefore, $\tan(\theta) = -\sqrt{3}$. The angle whose tangent is $\sqrt{3}$ is $60^\circ$. Since the slope is negative, the line is descending from left to right, but the question asks for the acute angle it forms with the x-axis, which is $60^\circ$.

Find the Acute Angle That Is Formed by the Line y−3x+1=0y - \sqrt { 3 } x + 1 = 0y−3​x+1=0

Find the Acute Angle That Is Formed by the Line $y - \sqrt { 3 } x + 1 = 0$