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

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:

$\angle A$
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:

1594290351178
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.

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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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