RD Sharma Class 11 Chapter 10 Solutions (Sine And Cosine Formulae And Their Applications)
RD Sharma Class 11 Maths Solutions Chapter 10 Sine and Cosine Formulae and their Applications provides you with an in-depth understanding of the concepts of trigonometric relations of a triangle. In this RD Sharma Class 11 Maths Solutions Maths chapter, we will learn about the Sine and Cosine formula and their applications with 4 exercises along with detailed solutions to the questions in each of the exercises. Apart from the laws of sine and cosine rule, you would also learn the projection formulae, Napier’s analogy or the law of tangents and Area of a triangle.
This chapter has a total of 68 questions divided into 4 sections, which covers the topic extensively. Along with objective type questions, there are simple questions that require you to find out the ratio of the sides of a triangle based on the angles and length or finding the sin A, sin A, sin C given their lengths by using the different sine and cosine rules. There are some difficult problems too which involve proving complex formulas using simple rules.
InstaSolv provides solutions to these questions in a way that will clear up many of your doubts. They are explained in the simplest language which is very easily understandable. The subject matter experts have explained in steps how to derive the answer which will also help clear all the concepts related to trigonometry.
Topics Covered in RD Sharma Solutions for Class 11 Maths Chapter 10 Sine And Cosine Formulae
Area of a Triangle Rule
- There are many ways to find the area of a triangle, based on the information given:
- If we know the base and the height, then Area = ½ * base * height
- If we know all the 3 sides then first calculate half of the perimeter and then we can deduct the area:Perimeter = side a + side b + side c s = perimeter / 2 = (side a + side b + side c) / 2 Area of Triangle = √s (s-a) (s-b) (s-c)
- Knowing 2 sides and the included angle – If we know sides x, y and angle Z (included angle): Area = ½ * x * y * Sin Z
We have similar equations given other sides and included angle:
Area = ½ * y * z * Sin X
Area = ½ * x * z * Sin Y
- The Cosine Rule
In any triangle with sides x, y, and z, the law of Cosine tells us that:
z² = x² + y² – 2xy Cos Z
‘Z’ is the angle opposite the side z.
This rule is useful when we are trying to relate all the 3 sides to 1 angle.
- The Sine Rule
For a triangle with sides x, y, and z, the law of Sine tells us that:
‘z’ is the hypotenuse and x, y is the other 2 sides of the right triangle.
- Projection Formula
In any triangle with angles X, Y, and Z and sides x, y, and z (where x is the side opposite to angle X, y is the side opposite to angle Y, and z is the side opposite to angle Z) :
y Cos Z + z Cos Y = X
x Cos Z + z Cos X = Y
x Cos Y + y Cos X = Z
This formula gives the relationship between angles and the sides of a triangle and we can use this to find the length of the side of a triangle if the other 2 sides and their corresponding angles are known.
- Napier’s Analogy or the Law of Tangents
In any triangle with sides x, y, z and angles X, Y, Z, the law of tangent states:
Tan( (X-Y / 2) = ((x-y)/(x+y)) cot Z/2
You can apply the same rule by replacing sides and angles with the values given in the problem. Here Cot is the cotangent.
Discussion of Exercises of RD Sharma Solutions for Class 11 Maths Chapter 10
- The questions in the first exercise help you hone your knowledge of Sin and Cosine rule by applying them in different ways to find out the sides and angles of the triangle. It has 31 questions.
- The second set of exercises has questions related to the area of a triangle where you get to apply them in different ways. It has 19 questions.
- The 3rd set has very short answers which have a mix of all the concepts; area of a triangle, sin and cosine rules. It has 10 questions.
- The MCQ section is an objective type where you are given a problem with 4 possible answers and you have to select one based on your derivations.
- The questions by RD Sharma Solutions will gear you to take any exams like JEE or NEET and form a good base for the board exams. It has detailed illustrations with many examples which will clear your concepts of different trigonometric functions.
Benefits of RD Sharma Solutions for Class 11 Maths Chapter 10 by InstaSolv
- InstaSolv has made it easy for you to get the most basic as well as complex concepts of Sin and Cosine rule with an algorithmic approach to solve each problem.
- The free InstaSolv solutions will aid you in managing your time effectively while solving the problems.