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Some Applications of Trigonometry Class 10th Notes - Free NCERT Class 10 Maths Chapter 9 Notes - Download PDF

Some Applications of Trigonometry Class 10th Notes - Free NCERT Class 10 Maths Chapter 9 Notes - Download PDF

Edited By Ramraj Saini | Updated on Mar 19, 2022 12:34 PM IST

The NCERT Class 10 Maths chapter 9 notes covers an outline of the chapter some application of trigonometry. Trigonometry is used in many ways in the things around us, we can use it for calculating the height and distance of some objects without actually measuring them.

Line of Sight

When looking at some object then the line made by our vision to the object is the Line of Sight.

Line of Sight

Horizontal Line

It is a distance between the observer and the object.

Angle of Elevation

It is the angle made by the line of sight to the top of the object and the horizontal line. It lies above the horizontal line that is the angle of elevation made when looking up to the object.

Angle of Depression

It is made when the observer needs to look down to see the object. The angle between the horizontal line and the line of sight is the angle of depression.

Angle of Depression

Consider the figure below:

1644385644942

Example 1:

What is the value of sinθ/cosθ?

sinθ/cosθ=(Opposite/Hypotenuse)/(Adjacent/Hypotenuse)=tanθ

Trigonometry ratio table:

\angle A

0^o

30^o

45^o

60^o

90^o

Sin A

0

\frac{1}{2}

\frac{1}{\sqrt{2}}

\frac{\sqrt{3}}{2}

1

Cos A

1

\frac{\sqrt{3}}{2}


\frac{1}{2}

0

Tan A

0

\frac{1}{\sqrt{3}}

1

\sqrt{3}

Not defined

Cosec A

Not defined

2

\sqrt{2}

\frac{2}{\sqrt{3}}

1

Sec A

1

\frac{2}{\sqrt{3}}

\sqrt{2}

2

Not defined

Cot A

Not defined

\sqrt{3}

1

\frac{1}{\sqrt{3}}

0

Example 2:

What is the value of cos 60-sin 30?

From the above table:

cos 60=1/2

sin 30=1/2

Then cos 60-sin 30=1/2-1/2=0

Example 3: From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high building are 45° and 60° respectively. Find the height of the tower.

Answer:

15942903511781594290349905
Suppose BC = his the height of the transmission tower and the AB be the height of the building and AD is the distance between the building and the observer point (D).We have,AB = 20 m, BC = hm and AD = xm

\angle CDA = 60^o

\angle BDA = 45^o

According to the question,
In triangle BDA,

\tan 45^o = \frac{AB}{AD}=\frac{20}{x}

x = 20 m

Again,
In triangle CAD,

\\\Rightarrow \tan 60^o = \frac{AB+BC}{AD}=\frac{20+h}{20}\\\\\Rightarrow \sqrt{3}= 1+\frac{h}{20}\\\\\Rightarrow h=20(\sqrt{3}-1)\\\\\Rightarrow 20(0.732) = 14.64 m

Answer- the height of the tower is 14.64 m

Significance of NCERT Class 10 Maths Chapter 9 Notes

Some Applications of Trigonometry class 10th notes will help to understand the formulas, statements, rules in detail. This NCERT Class 10 Maths chapter 9 notes also contains previous year’s questions and NCERT TextBook pdf. It also contains FAQ or frequently asked questions along with topic-wise explanations. In offline mode, Class 10 Maths chapter 9 notes pdf download can be used to prepare.

Class 10 Chapter Wise Notes

NCERT Solutions of Cass 10 Subject Wise

NCERT Class 10 Exemplar Solutions for Other Subjects:

Frequently Asked Questions (FAQs)

1. How many trigonometric ratios are there according to Class 10 Math’s chapter 9 notes?

There are 6 trigonometric ratios. They are, sine, cosine, tangent, cotangent, secant, cosecant.

2. What is the weightage of Class 10 some application of trigonometry in the board exam?

Students can expect 4 to 5 marks questions from the notes for Class 10 Math’s chapter 9.

3. What is the Angle of Depression ?

 It is made when the observer needs to look down to see the object. The angle between the horizontal line and the line of sight is the angle of depression. You can find this in some application of trigonometry class 10 notes pdf download. 

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A block of mass 0.50 kg is moving with a speed of 2.00 ms-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

Option 1)

0.34\; J

Option 2)

0.16\; J

Option 3)

1.00\; J

Option 4)

0.67\; J

A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times.  Assume that the potential energy lost each time he lowers the mass is dissipated.  How much fat will he use up considering the work done only when the weight is lifted up ?  Fat supplies 3.8×107 J of energy per kg which is converted to mechanical energy with a 20% efficiency rate.  Take g = 9.8 ms−2 :

Option 1)

2.45×10−3 kg

Option 2)

 6.45×10−3 kg

Option 3)

 9.89×10−3 kg

Option 4)

12.89×10−3 kg

 

An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

Option 1)

2,000 \; J - 5,000\; J

Option 2)

200 \, \, J - 500 \, \, J

Option 3)

2\times 10^{5}J-3\times 10^{5}J

Option 4)

20,000 \, \, J - 50,000 \, \, J

A particle is projected at 600   to the horizontal with a kinetic energy K. The kinetic energy at the highest point

Option 1)

K/2\,

Option 2)

\; K\;

Option 3)

zero\;

Option 4)

K/4

In the reaction,

2Al_{(s)}+6HCL_{(aq)}\rightarrow 2Al^{3+}\, _{(aq)}+6Cl^{-}\, _{(aq)}+3H_{2(g)}

Option 1)

11.2\, L\, H_{2(g)}  at STP  is produced for every mole HCL_{(aq)}  consumed

Option 2)

6L\, HCl_{(aq)}  is consumed for ever 3L\, H_{2(g)}      produced

Option 3)

33.6 L\, H_{2(g)} is produced regardless of temperature and pressure for every mole Al that reacts

Option 4)

67.2\, L\, H_{2(g)} at STP is produced for every mole Al that reacts .

How many moles of magnesium phosphate, Mg_{3}(PO_{4})_{2} will contain 0.25 mole of oxygen atoms?

Option 1)

0.02

Option 2)

3.125 × 10-2

Option 3)

1.25 × 10-2

Option 4)

2.5 × 10-2

If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

Option 1)

decrease twice

Option 2)

increase two fold

Option 3)

remain unchanged

Option 4)

be a function of the molecular mass of the substance.

With increase of temperature, which of these changes?

Option 1)

Molality

Option 2)

Weight fraction of solute

Option 3)

Fraction of solute present in water

Option 4)

Mole fraction.

Number of atoms in 558.5 gram Fe (at. wt.of Fe = 55.85 g mol-1) is

Option 1)

twice that in 60 g carbon

Option 2)

6.023 × 1022

Option 3)

half that in 8 g He

Option 4)

558.5 × 6.023 × 1023

A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t2) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m2 , the number of rotations made by the pulley before its direction of motion if reversed, is

Option 1)

less than 3

Option 2)

more than 3 but less than 6

Option 3)

more than 6 but less than 9

Option 4)

more than 9

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