CBSE Class 10thSome Applications of Trigonometry Details & Preparations Downloads

"Some Applications of Trigonometry" stands as a gateway to understanding the practical implications of trigonometric concepts. This chapter not only enriches mathematical knowledge but also demonstrates the real-world applications that make trigonometry an indispensable tool in various fields.

CBSE NCERT Download Unveiling Practical Insights with 'Some Applications of Trigonometry.

 The Foundation Brief Recap of Trigonometry Basics

Before delving into applications, it's crucial to revisit the fundamental principles of trigonometry introduced in earlier chapters. Concepts such as sine, cosine, tangent, and the Pythagorean theorem lay the groundwork for the practical applications that follow.

 Heights and Distances Practical Geometry Unveiled

One of the primary applications covered in Class 9 Chapter 9 is the use of trigonometry in determining heights and distances. Students learn how to calculate the height of tall structures, such as buildings or mountains, and the distance between objects using trigonometric ratios. This practical geometry application provides a hands-on understanding of trigonometry's relevance in everyday scenarios.

 Shadows and Elevation Angle  Timekeeping with Trigonometry

The chapter further explores the relationship between shadows and elevation angles. Students learn how to use trigonometric functions to calculate the time of the day based on the length of shadows. This application showcases the connection between trigonometry and timekeeping, a concept deeply rooted in ancient sundial technology.

Horizontal Level and Line of Sight

Line of sight is the line drawn from the eye of the observer to the point on the object viewed by the observer.

Angle of Elevation

The angle of elevation is relevant for objects above the horizontal level. It is the angle formed by the line of sight with the horizontal level. In the below-mentioned diagram, “θ” denotes the angle of elevation.

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Angle of Depression

The angle of depression is relevant for objects below the horizontal level. It is the angle formed by the line of sight with the horizontal level.

Measuring the Distances of Celestial bodies with the Help of Trigonometry

Large distances can be measured by the parallax method. The parallax angle is half the angle between two lines of sight when an object is viewed from two different positions. Knowing the parallax angle and the distance between the two positions, large distances can be measured.

Solved Examples

Example 1: A kite is flying at a height of 60 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60°. Find the length of the string, assuming that there is no slack in the string.

Solution

Let A be the position of a kite at a height of 60 m above the ground.

Thus, AB = 60 m

Also, AC is the length of the string.

Angle of inclination = ∠ACB = 60

In the right triangle ABC,

sin 60° = AB/AC

√3/2 = 60/AC

AC = (60 × 2)√/3

= (120 × √3)/(√3 × √3)

= (120√3)/3

= 40√3

Therefore, the length of the string is 40√3 m.

CBSE Class 10 NCERT Mathematics Topics for a Strong Foundation (NCERT DOWNLOAD)

Applications in Navigation: Sailing the Seas of Trigonometry

Trigonometry finds its way into navigation, where sailors use it to determine their ship's location and course. By understanding the angles of elevation and depression, students gain insights into how trigonometry plays a crucial role in ensuring accurate navigation on the high seas.

 Beyond the Classroom: Practical Insights and Future Applications

The blog concludes by emphasizing the real-world relevance of mastering trigonometry. From architecture and surveying to astronomy and technology, the applications of trigonometry extend far beyond the classroom. Understanding its practical uses not only enhances academic performance but also equips students with valuable skills for future endeavors.

Example 2

 A circus artist is climbing a 20 m-long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is 30°. (see fig. 9.11)

Solution:

The length of the rope is 20 m and the angle made by the rope with the ground level is 30°.

Given: AC = 20 m and angle C = 30°

To Find: Height of the pole

Let AB be the vertical pole

In right ΔABC, using sine formula

sin 30° = AB/AC

Using value of sin 30 degrees is ½, we have

1/2 = AB/20

AB = 20/2

AB = 10

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FAQ

Q1 Where trigonometry is used in real life?

Ans Trigonometry and its functions have an enormous number of uses in our daily life. For instance, it is used in geography to measure the distance between landmarks, in astronomy to measure the distance of nearby stars and also in the satellite navigation system.

Q2 How is trigonometry used in day to day life?

Ans Trigonometry is also used in Astronomy, Navigation system, Surveying, Architecture, CT scans, and ultrasounds, Number theory, oceanography, computer graphics, and in-game development.

Q3 What is the conclusion of trigonometry?

Ans Conclusion: Trigonometry, often seen as an abstract mathematical concept, finds practical applications in various aspects of our lives. From architecture and engineering to navigation and computer graphics, the principles of trigonometry help us solve problems, measure distances, and understand the world around us.

Q4 How does NASA use trigonometry?

Ans Thanks to trigonometry we know the distances between the planets from the Earth. When an astronaut needs to calculate the speed they are moving in the spacecraft, if they already know the distance from a particular location they can use trigonometry to calculate the unknown distance to another location point.

Q5 Who is the father of trigonometry *?

Ans  Hipparchus is referred to as the father of trigonometry and was a Greek astronomer. Trigonometry is a branch of mathematics that studies the angles of sides of triangles.