# 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. Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

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