A line makes an angle of 30° with the positive direction of X- axis. So the slope of the line is .......... . (A) 1/ 2 (B) 3 /2 (C) 1/3 (D) 3
(4) A line makes an angle of 30° with the positive direction of X- axis. So the slope of the line is ………. .
(A) 1/ 2 (B) 3 /2 (C) 1/3 (D) 3
Slope of line will be
\[\tan30° = \frac{1}{\sqrt{3}}\]
Hence, the correct answer is \[\frac{1}{\sqrt{3}}\] .
Explanation:-
The given problem is to find the slope of a line that makes an angle of 30 degrees with the positive direction of x-axis.
We know that the tangent of an angle is defined as the ratio of the opposite side to the adjacent side of a right triangle. In this case, if we consider the line as the hypotenuse of the right triangle, then the slope of the line is equal to the tangent of the angle it makes with the positive direction of x-axis.
So, we have the angle as 30 degrees, which can also be represented in radians as π/6. The tangent of 30 degrees is given by:
tan(30 degrees) = tan(π/6) = 1/√3
Therefore, the slope of the line is 1/√3 or √3/3 in rationalized form.
Chapter 5. Co-ordinate Geometry -Problem set 5 (Page 122)