Angles made by the line with the positive direction of X-axis are given. Find the slope of these lines. (1) 45° (2) 60° (3) 90°

Answer:-

1.   60 degree 

m= tan 60 = √3

Thus Slope = √3

Explanation:-

The slope of a line is defined as the change in y divided by the change in x between any two points on the line. When we have the angle that the line makes with the positive direction of the X-axis, we can use trigonometry to find the slope of the line.

1. For an angle of 45 degrees, we know that it forms an isosceles right triangle with the X-axis. The slope of the line can be found by taking the tangent of the angle. Mathematically, this can be expressed as:

[slope = \tan(45^{\circ}) = \frac{\sin(45^{\circ})}{\cos(45^{\circ})} = \frac{1}{1} = 1]

Therefore, the slope of a line that makes an angle of 45 degrees with the positive direction of the X-axis is 1.

2. For an angle of 60 degrees, we can draw a right triangle with the X-axis and the line. We can then use trigonometry to find the slope of the line. We know that the tangent of 60 degrees is equal to the square root of 3 divided by 1.

[slope = \tan(60^{\circ}) = \frac{\sin(60^{\circ})}{\cos(60^{\circ})} = \frac{\sqrt{3}}{1}]

Therefore, the slope of a line that makes an angle of 60 degrees with the positive direction of the X-axis is [\sqrt{3}].

3. For an angle of 90 degrees, the line is perpendicular to the X-axis. The slope of a perpendicular line is the negative reciprocal of the slope of the original line. Since the original line is parallel to the Y-axis, it has an undefined slope. The slope of a perpendicular line is 0.

Therefore, the slope of a line that makes an angle of 90 degrees with the positive direction of the X-axis is 0.