**Angle of inclination worksheet :**

Angle of inclination worksheet is much useful to the students who would like to practice problems on angles.

1) Find the angle of inclination of the straight line whose slope is 1/√3.

2) If the angle of inclination of a straight line is 45°, find its slope.

3) If the angle of inclination of a straight line is 30°, find its slope.

4) Find the angle of inclination of the straight line whose slope is √3.

5) Find the angle of inclination of the straight line whose equation is y = x + 32.

**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, m = tan θ

Given : Slope = 1/√3

So, we have

tan θ = 1/√3

θ = 30°

**Hence, 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 = tan θ

Given : θ = 45°

Then, we have

m = tan 45°

m = 1

**Hence, 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 = tan θ

Given : θ = 30°

Then, we have

m = tan 30°

m = 1/√3

**Hence, 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 = tan θ

Given : Slope = √3

So, we have

tan θ = √3

θ = 60°

**Hence, 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, m = tan θ

So, we have

tan θ = 1

θ = 45°

**Hence, the angle of inclination is 45° **

To understand and solve the problems given in the above worksheet, we have to know the following important stuff about angle of inclination of a line.

Now, let us look at the stuff about angle of inclination of a line.

Let a straight line l intersect the x - axis at A. The angle between the positive x - axis and the line l, measured in counter clockwise direction is called the angle of inclination of the straight line l.

In the above figure, If θ is the angle of a straight line l, then we have the following important points.

(i) 0° ≤ θ ≤ 180°

(ii) For horizontal lines, θ = 0° or 180° and for vertical lines, θ = 90°

(iii) If a straight line initially lies along the x-axis and starts rotating about a fixed point A on the x-axis in the counter clockwise direction and finally coincides with the x-axis, then the angle of inclination of the straight line in the initial position is 0°and that of the line in the final position is 0°.

(iv) Lines which are perpendicular to x-axis are called as vertical lines.

(v) Lines which are perpendicular to y-axis are called as horizontal lines.

(vi) Other lines which are neither perpendicular to x- axis and nor to y-axis are called as slant lines.

The major application of angle of inclination of a straight line is finding slope.

If θ is the angle of inclination of a straight line l, then tanθ is called the slope of gradient of the line is denoted by "m".

Therefore, the slope of the straight line is

**m = tan θ**

for 0° ≤ θ ≤ 180°

Let us find the slope of a straight using the above formula

(i) For horizontal lines, the angle of inclination is 0° or 180°. That is, θ = 0° or 180°

Therefore, slope of the straight line is

m = tan0° or tan 180° = 0

(ii) For vertical lines, the angle of inclination is 90°. That is θ = 90°

Therefore, slope of the straight line is

m = tan90° = Undefined

(iii) For slant lines, if θ is acute, then the slope is positive. Whereas if θ is obtuse, then the slope is negative.

When we look at a straight line visually, we can come to know the sign of the slope easily.

To know the sign of slope of a straight line, always we have to look at the straight line from left to right.

The figures given below illustrate this.

After having gone through the stuff given above, we hope that the students would have understood "Angle of inclination worksheet".

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