ANGLE OF INCLINATION WORKSHEET 

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

Solutions

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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