Problem 1 :
Find the angle of inclination of the straight line whose slope is 1/√3.
Problem 2 :
If the angle of inclination of a straight line is 45°, find its slope.
Problem 3 :
If the angle of inclination of a straight line is 30°, find its slope.
Problem 4 :
Find the angle of inclination of the straight line whose slope is √3.
Problem 5 :
Find the angle of inclination of the straight line whose equation is y = x + 32.
Problem 6 :
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
Problem 1 :
Find the angle of inclination of the straight line whose slope is 1/√3.
Solution :
Let θ be the angle of inclination of the line.
Then, slope of the line is
m = tanθ
Given : Slope = 1/√3
Then,
1/√3 = tanθ
θ = 30°
So, the angle of inclination is 30°.
Problem 2 :
If the angle of inclination of a straight line is 45°, find its slope.
Solution :
Let θ be the angle of inclination of the line.
Then, slope of the line,
m = tanθ
Given : θ = 45°
Then,
m = tan 45°
m = 1
So, the slope is 1.
Problem 3 :
If the angle of inclination of a straight line is 30°, find its slope.
Solution :
Let θ be the angle of inclination of the line.
Then, slope of the line,
m = tanθ
Given : θ = 30°
Then,
m = tan30°
m = 1/√3
So, the slope is 1/√3.
Problem 4 :
Find the angle of inclination of the straight line whose slope is √3.
Solution :
Let θ be the angle of inclination of the line.
Then, slope of the line,
m = tanθ
Given : Slope = √3
Then,
√3 = tanθ
θ = 60°
So, the angle of inclination is 60°.
Problem 5 :
Find the angle of inclination of the straight line whose equation is y = x + 32.
Solution :
Let θ be the angle of inclination of the line.
The given equation is in slope intercept form.
That is,
y = mx + b
Comparing
y = x + 32
and
y = mx + b,
we get the slope m = 1.
We know that the slope of the line is
m = tanθ
Then,
1 = tanθ
θ = 45°
So, the angle of inclination is 45°.
Problem 6 :
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 :
Because the side AB is parallel to x-axis, angle formed by the side AB with x-axis is zero.
Then,
m = tan 0°
m = 0
So, the slope of the side 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.
Then,
m = tan 90°
m = undefined
So, the slope of the side BC is undefined.
(ii) Slope of the diagonal AC :
Because AC is diagonal, the angle of inclination of the diagonal AC with x-axis is 45°.
Then,
m = tan 45°
m = 1
So, the slope of the diagonal AC is 1.
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