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RD Sharma Class 10 Chapter 12 Solutions (Some Applications of Trigonometry)

RD Sharma Class 10 Maths Solutions Chapter 12 – Some Applications of Trigonometry is one of the most recommended study material. You will learn the use of Trigonometry in finding the distances and heights of numerous objects, without actually measuring them. In this chapter, you learn about concepts of the line of sight, angle of elevation and angle of depression in formulating trigonometric expressions and use of trigonometric identities to solve the expressions for required values.

While solving all the 72 questions asked in only 1 exercise of Chapter 12 of RD Sharma Class 10 Maths Solutions, you learn how to make an imaginary right angle using the height of the object and line of sight using the information given in a question. Here, distance is usually the base of the imaginary triangle or length of the horizontal level. The questions ask you to imagine that the hypotenuse of the triangle is actually the line of sight. For determination of the angle of elevation or depression, you need to use the trigonometric ratios and identities. For solving some complex questions for the distance between two objects from a single point, you need to create/imagine two right-angled triangles. These two triangles have common heights, or they may be two merged triangles such as one right-angled triangle lying inside another right-angled triangle.

Our RD Sharma solutions answer all questions of the exercise in a logical and step by step manner. They help you to strengthen your conceptual foundation and move ahead with concrete knowledge to higher classes. Preparation for board exams becomes an easy task when you follow our RD Sharma solutions for the exercise given in chapter 12 of RD Sharma Class 10 Maths Book. Our Solutions help you learn and revise all the concepts quickly and efficiently.

RD Sharma Class 10 Maths Some Applications of Trigonometry: Important Topics

Chapter 12 of RD Sharma Class 10 Maths teaches you how to apply the knowledge of Trigonometry. You come to know about the useful tools and methods for studying and performing calculations in the areas related to engineering, navigation, constructing maps, geography, astronomy, among others. Some topics in this chapter have been discussed below.

 

  • Heights and Distances

 

This part tells about the applications of Trigonometry in theory and in real-life situations. Here you learn about calculating heights of big buildings when the angle of elevation and distance is given, without actually measuring it. You will also learn how to determine the angles of elevation and depression along with the distance to a far lying object using the other information given in the questions. 

In this chapter, you will learn various significant terms, such as the following.

 

  • Line of Sight

 

Here you will learn that the line of sight is the line made from the eye of the person who is viewing to the point in the object being viewed.

 

  • Angle of elevation

 

This section tells you that the angle of elevation of the point observed, is the angle made by the line of sight with the plane when the point being seen is above the horizontal level, i.e., the case when we elevate our head to look at the object.

 

  • Angle of Depression

 

This portion of the chapter tells you that the angle of depression of a point on the thing being observed is the angle formed by the line of vision with the horizontal level when the point is lower than the horizontal level. This is same as the situation when an observer lowers his head to see the point being viewed.

This chapter also covers in details many other topics from this chapter. 

RD Sharma Class 10 Maths Chapter 12: Exercise-Discussion

There is a single exercise containing 72 questions in this chapter. Our RD Sharma Class 10 Maths Solutions Chapter 12 – Some Applications of Trigonometry are concise, clear and accurate. The constituents of the exercise have been discussed below. 

Exercise 12.1

  • There are 72 questions in this exercise. 
  • Question 1 asks you to calculate the height of the tower when the horizontal distance between the base of the tower and the angle of elevation is given. 
  • In questions 2, 4, 5 and 8 the height of object and angle of elevation is given, and the hypotenuse of the imaginary right-angled triangle is to be determined. 
  • Questions 3, 6, 19, 36 and 37 ask you to calculate the height of the imaginary triangle formed while solving the question when the horizontal distance and the angle of elevation are provided in the question. Questions 7, 9, 12, 18, 20, 21, 24, 26, 34, 35, 47 and 48 ask you to determine the height by imaging two right triangles, one lying inside the other. 
  • Questions 10, 13, 14 and 29 ask you to determine horizontal distance by imaging two right triangles, one lying inside the other. 
  • Questions 11, 31, 33, 38, 54 and 56 asks you to determine the height of the tower by imagining two right triangles placed back to back to each other. 
  • Questions 17 and 27 asks to find the height and the distance between two given points. Questions 25, 53, 57 and 59 asks you to determine the distance between two buildings using information about the angle of depression.  
  • Questions 28, 42 and 46 ask you to calculate height when the angle of elevation from ground and angles of depression from a higher point is given. 
  • Questions 30, 44, 45, 50, 52 and 55 ask you to determine the height of one of the right triangles when two right triangles are placed in such a way that both have the same base. Question 39 asks to determine the height and length of the base when both are equal. 
  • Question 51 asks you to determine height when two different angles of elevation are given from two different points. 
  • Questions 60 to 72 are slightly complex problems using your higher-order thinking skills based on the concepts learnt and used till now.  

Benefits of RD Sharma Class 10 Maths Solutions for Chapter 12 – Some Applications of Trigonometry

Some of the key benefits of learning and revising from RD Sharma Class 10 Maths Solutions Chapter 12 – Some Applications of Trigonometry are listed below.

  • Our RD Sharma Solutions help you in quick, and effective learning and revision during exams. 
  • They are prepared in a step by step manner so that you can understand learn and remember them easily.
  • They help you build a sound conceptual base so that you can learn more complex concepts in higher classes. 
  • The solutions provide you with enough practice to help you become thorough with all the concepts covered in chapter 12.
  • They cover all possible question types from this chapter that are important from exam point of view.