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RD Sharma Class 10 Chapter 5 Solutions (Trigonometric Ratios)

RD Sharma Class 10 Maths Solutions Chapter 5 – Trigonometric Ratios have been prepared to help you prepare well for the CBSE Class 10 Board exams. These Solutions cover all aspects of Trigonometric Ratios based on relationships between the sides and angles of a triangle. Trigonometry is used to measure heights and lengths of bigger objects and distances which are otherwise difficult to measure with normal tools. This Chapter mentions that ratios of the sides of a right triangle with respect to its acute angles are known as Trigonometric Ratios of the angle.

This Chapter RD Sharma Class 10 Maths Solutions Book has a total of 3 exercises containing 87 questions. Here you learn how to determine the values of Trigonometric Ratios in a triangle when the measurement of sides is given or other Trigonometric Ratios for a triangle are given. You also learn how to find out values of Trigonometric Ratios using an equation formulated with related trigonometric ratio terms. In this Chapter, some questions need you to proof some relationships based on the Trigonometric Ratios of a triangle and some need you to evaluate the given equations containing Trigonometric Ratios for specific angles. All of these questions have been solved in our RD Sharma Class 10 Maths Solutions Chapter 5 in a step by step manner for you.

Solutions of RD Sharma Class 10 Maths Trigonometric Ratios are the best study resource for revision of the topics covered in this Chapter. They are just what you need to ace your Class 10 board exams. These Solutions follow a logical flow and at the same are easy to understand and learn.

Class 10 Maths Trigonometric Ratios

Trigonometry is a study of relationships between the angles and sides of a given triangle. Here you learn that ratios of the sides of a right triangle with respect to its acute angles are known as Trigonometric Ratios for that angle.

The detailed description of the points covered in this Chapter is given below.

  • Trigonometric Ratios

This chapter teaches you that the Trigonometric Ratios of an acute angle in a right-angle triangle mention the relationship among the angle and the length of its sides. Imagine a triangle ABC right angled at B, the ratios are defined with respect to either of the acute angle ‘A’ or ‘C’. The angle may be called as ‘θ’.

The 6 Trigonometric Ratios with respect to the sides of a chosen angle A are given as –

sin A = side opposite to angle A/ hypotenuse 

cos A = side next to to angle/ hypotenuse

tan A = side opposite to angle A/side adjacent to angle A.

cosec A = 1/sin A; sec A = 1 / cos A; tan A = 1/ cot A; tan A = sin A/ cos A 

Knowing one of the Trigonometric Ratios of an acute angle, we come to know about the remaining Trigonometric Ratios of the angle also. There is no change in values related to Trigonometric Ratios of an angle when we change the measurements of the sides of the triangle, in case the angle remains the same. 

 

  • Trigonometric Ratios of Some Specific Angles 

 

Here you learn to derive the particular numerical values for Trigonometric Ratios for 0°, 30°, 45°, 60° and 90°. You also come to know that sin A increases from 0 to 1 whereas cos A decreases from 1 to 0 when angling A increases from 0° to 90°. 

 

  • Trigonometric Ratios of Complementary Angles 

 

In this section of the Chapter, you will learn that we call any two angles of complementary angles when their sum is equal to 90°. In a right-angled triangle the other two angles except for the right angle, have the sum of 90° and hence they are complementary to each other. So in general, sin (90° – A) = cos A, cos (90° – A) = sin A; tan (90° – A) = cot A, cot (90° – A) = tan A; sec (90° – A) = cosec A, cosec (90° – A) = sec A; for all the values of angle A lying between 0° and 90°. 

RD Sharma Class 10 Maths Chapter 7 Exercises

Our Solutions are the best study material available for all concepts covered by RD Sharma Solutions Class 10 Maths Chapter 7. The main components of all the three exercises of this Chapter are given below – 

Exercise 5.1 

This exercise has 36 questions. Question 1 asks you to determine the value of a trigonometric ratio for a triangle when another ratio is given. Questions 2 and 6 ask to determine the value of a trigonometric ratio when the measurement of sides of a triangle are provided. Question 3 asks to prove the equality of Trigonometric Ratios for a triangle. Questions 3 to 5 and 7 to 36 ask you to find out values of Trigonometric Ratios using an equation formulated with related trigonometric ratio terms.

Exercise 5.2

This exercise consists of 40 questions and all of them ask you to evaluate the equations containing Trigonometric Ratios for specific angles like 30°, 45°, 60° and 90° among others. Some of the questions involve geometrical figures like triangles and rectangles also. 

Exercise 5.3 

This exercise contains 11 questions. Questions 1 and 2 ask you to evaluate equations based on Trigonometric Ratios. Question 3 asks you to express the equation based on Trigonometric Ratios of an angle in terms of angles between 0° and 30°. Questions 4 and 11 ask you to find the value of an unknown angle in the given equation. Question 5 to 7 ask you to prove equalities among the given trigonometric equations. Question 8 to 10 asks you to determine the degree measure of an angle in the given equation. 

Benefits of RD Sharma Class 10 Maths Solutions for Chapter 5 – Trigonometric Ratios

  • Solutions of all the questions are written using the best available strategies to answer these questions and let you grasp the concepts quickly and effectively.
  • These are easy to understand and remember.
  • They help you in revising the contents thoroughly during exams and score more marks in Class 10 board exams.
  • They help you build a solid conceptual foundation at this level in this area of mathematics so that you find it easy to apply the concepts learnt now in higher grades.
  • They comprehensively all concepts covered in your Class 10 Maths Syllabus, to ensure you don’t miss out on anything. 
  • They have been drafted in a manner to make learning Maths fun, interesting, stimulating and a happy process.