HOW TO FIND THE SLOPE WITH ANGLE OF INCLINATION
About "How to find the slope with angle of inclination"
How to find the slope with angle of inclination :
Actually we follow four methods to find the slope of the line
(i) Slope using angle of inclination (m = tan θ)
(ii) Slope with two points lies on the line
m = (y2 - y1)/(x2-x1)
(iii) Slope by comparing the equation with y = mx + b
(iv) Slope using the formula
m = -coefficient of y/coefficient of x
Here we are going to see how to find the slope with angle of inclination.
Example 1 :
Find the slope of the straight line whose angle of inclination is 30°
Solution :
Angle of inclination (θ) = 30°
Slope (m) = tan θ
Instead of applying θ as 30°, we get
m = tan 30°
m = 1/√3
Example 2 :
Find the slope of the straight line whose angle of inclination is 60°
Solution :
Angle of inclination (θ) = 60°
Slope (m) = tan θ
Instead of applying θ as 60°, we get
m = tan 60°
m = √3
Example 3 :
Find the slope of the straight line whose angle of inclination is 90°
Solution :
Angle of inclination (θ) = 90°
Slope (m) = tan θ
Instead of applying θ as 90°, we get
m = tan 90°
m = ∞
Example 4 :
Find the slope of the straight line whose angle of inclination is 45°
Solution :
Angle of inclination (θ) = 45°
Slope (m) = tan θ
Instead of applying θ as 45°, we get
m = tan 45°
m = 1
Example 5 :
The side AB of a square ABCD is parallel to x-axis . Find the
(i) slope of AB
(ii) slope of BC
(iii) slope of the diagonal AC
Solution :
(i) Slope of AB
Since the side AB is parallel to x-axis, angle formed by the side AB with x-axis is zero.
So, slope of the side AB (m) = tan 0° = 0
Hence slope of AB is 0.
(ii) Slope of BC :
If the side AB is parallel to x-axis, then the side BC will be perpendicular to x-axis.
So it forms the angle 90° with axis.
m = tan 90° = ∞
Hence the slope of the side BC is ∞
(ii) Slope of the diagonal AC :
Since the side AC is diagonal, the angle of inclination of the side AC with x-axis is 45°
m = tan 45° = 1
Hence the slope of the side AC is 1.
After having gone through the stuff given on "How to find the slope with angle of inclination", we hope that the students would have understood how to solve problems using unit rates.
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