# 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.

You can also visit the following web pages on different stuff in math.

WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6 