Commerce Exam > Commerce Notes > Mathematics (Maths) Class 11 > RD Sharma Solutions Commerce Maths Class 11 Class 11 Solutions Chapter - Sine
RD Sharma Solutions Commerce Maths Class 11 Class 11 Solutions Chapter - Sine
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Page 1 10. Sine and Cosine Formulae and their Applications Exercise 10.1 1. Question If in a ?ABC, ?A = 45 o , ?B = 60 o , and ?C = 75 o ; find the ratio of its sides. Answer Let a, b, c be the sides of the given triangle. Then by applying the sine rule, we get Now substituting the given values we get (? sin (a + b) = sin a cos b + sin b cos a) Now substituting the corresponding values, we get, Multiplying 2v2, we get Hence the ratio of the sides of the given triangle is 2. Question If in any ?ABC, ?C = 105 o , ?B = 45 o , a = 2, then find b. Answer Page 2 10. Sine and Cosine Formulae and their Applications Exercise 10.1 1. Question If in a ?ABC, ?A = 45 o , ?B = 60 o , and ?C = 75 o ; find the ratio of its sides. Answer Let a, b, c be the sides of the given triangle. Then by applying the sine rule, we get Now substituting the given values we get (? sin (a + b) = sin a cos b + sin b cos a) Now substituting the corresponding values, we get, Multiplying 2v2, we get Hence the ratio of the sides of the given triangle is 2. Question If in any ?ABC, ?C = 105 o , ?B = 45 o , a = 2, then find b. Answer We know in a triangle, ?A + ?B + ?C = 180° ? ?A = 180° - ?B - ?C Substituting the given values, we get ?A = 180° - 45° - 105° ? ?A = 30° Let a, b, c be the sides of the given triangle. Then by applying the sine rule, we get Now substituting the corresponding values we get Substitute the equivalent values of the sine, we get Hence the value of b is 2v2 units. 3. Question In ?ABC, if a = 18, b = 24 and c = 30 and ?C = 90 o , find sin A, sin B and sin C. Answer Let a, b, c be the sides of the given triangle. Then by applying the sine rule, we get Page 3 10. Sine and Cosine Formulae and their Applications Exercise 10.1 1. Question If in a ?ABC, ?A = 45 o , ?B = 60 o , and ?C = 75 o ; find the ratio of its sides. Answer Let a, b, c be the sides of the given triangle. Then by applying the sine rule, we get Now substituting the given values we get (? sin (a + b) = sin a cos b + sin b cos a) Now substituting the corresponding values, we get, Multiplying 2v2, we get Hence the ratio of the sides of the given triangle is 2. Question If in any ?ABC, ?C = 105 o , ?B = 45 o , a = 2, then find b. Answer We know in a triangle, ?A + ?B + ?C = 180° ? ?A = 180° - ?B - ?C Substituting the given values, we get ?A = 180° - 45° - 105° ? ?A = 30° Let a, b, c be the sides of the given triangle. Then by applying the sine rule, we get Now substituting the corresponding values we get Substitute the equivalent values of the sine, we get Hence the value of b is 2v2 units. 3. Question In ?ABC, if a = 18, b = 24 and c = 30 and ?C = 90 o , find sin A, sin B and sin C. Answer Let a, b, c be the sides of the given triangle. Then by applying the sine rule, we get Now substituting the given values we get Similarly, Now substituting the given values we get And given ?C = 90°, so sin C = sin 90° = 1. Hence the values of sin A, sin B, sin C are respectively 4. Question In any triangle ABC, prove the following: Answer Let a, b, c be the sides of any triangle ABC. Then by applying the sine rule, we get ?a = k sin A Similarly, b = k sin B So, a - b = k(sin A - sin B) And a + b = k(sin A + sin B) Page 4 10. Sine and Cosine Formulae and their Applications Exercise 10.1 1. Question If in a ?ABC, ?A = 45 o , ?B = 60 o , and ?C = 75 o ; find the ratio of its sides. Answer Let a, b, c be the sides of the given triangle. Then by applying the sine rule, we get Now substituting the given values we get (? sin (a + b) = sin a cos b + sin b cos a) Now substituting the corresponding values, we get, Multiplying 2v2, we get Hence the ratio of the sides of the given triangle is 2. Question If in any ?ABC, ?C = 105 o , ?B = 45 o , a = 2, then find b. Answer We know in a triangle, ?A + ?B + ?C = 180° ? ?A = 180° - ?B - ?C Substituting the given values, we get ?A = 180° - 45° - 105° ? ?A = 30° Let a, b, c be the sides of the given triangle. Then by applying the sine rule, we get Now substituting the corresponding values we get Substitute the equivalent values of the sine, we get Hence the value of b is 2v2 units. 3. Question In ?ABC, if a = 18, b = 24 and c = 30 and ?C = 90 o , find sin A, sin B and sin C. Answer Let a, b, c be the sides of the given triangle. Then by applying the sine rule, we get Now substituting the given values we get Similarly, Now substituting the given values we get And given ?C = 90°, so sin C = sin 90° = 1. Hence the values of sin A, sin B, sin C are respectively 4. Question In any triangle ABC, prove the following: Answer Let a, b, c be the sides of any triangle ABC. Then by applying the sine rule, we get ?a = k sin A Similarly, b = k sin B So, a - b = k(sin A - sin B) And a + b = k(sin A + sin B) So, the given LHS becomes, But, Substituting the above values in equation (i), we get Rearranging the above equation we get, Hence proved 5. Question In any triangle ABC, prove the following: Answer Let a, b, c be the sides of any triangle ABC. Then by applying the sine rule, we get ?a = k sin A Similarly, b = k sin B So, a - b = k(sin A - sin B)..(i) So the given LHS becomes, Page 5 10. Sine and Cosine Formulae and their Applications Exercise 10.1 1. Question If in a ?ABC, ?A = 45 o , ?B = 60 o , and ?C = 75 o ; find the ratio of its sides. Answer Let a, b, c be the sides of the given triangle. Then by applying the sine rule, we get Now substituting the given values we get (? sin (a + b) = sin a cos b + sin b cos a) Now substituting the corresponding values, we get, Multiplying 2v2, we get Hence the ratio of the sides of the given triangle is 2. Question If in any ?ABC, ?C = 105 o , ?B = 45 o , a = 2, then find b. Answer We know in a triangle, ?A + ?B + ?C = 180° ? ?A = 180° - ?B - ?C Substituting the given values, we get ?A = 180° - 45° - 105° ? ?A = 30° Let a, b, c be the sides of the given triangle. Then by applying the sine rule, we get Now substituting the corresponding values we get Substitute the equivalent values of the sine, we get Hence the value of b is 2v2 units. 3. Question In ?ABC, if a = 18, b = 24 and c = 30 and ?C = 90 o , find sin A, sin B and sin C. Answer Let a, b, c be the sides of the given triangle. Then by applying the sine rule, we get Now substituting the given values we get Similarly, Now substituting the given values we get And given ?C = 90°, so sin C = sin 90° = 1. Hence the values of sin A, sin B, sin C are respectively 4. Question In any triangle ABC, prove the following: Answer Let a, b, c be the sides of any triangle ABC. Then by applying the sine rule, we get ?a = k sin A Similarly, b = k sin B So, a - b = k(sin A - sin B) And a + b = k(sin A + sin B) So, the given LHS becomes, But, Substituting the above values in equation (i), we get Rearranging the above equation we get, Hence proved 5. Question In any triangle ABC, prove the following: Answer Let a, b, c be the sides of any triangle ABC. Then by applying the sine rule, we get ?a = k sin A Similarly, b = k sin B So, a - b = k(sin A - sin B)..(i) So the given LHS becomes, Substituting equation (i) in above equation, we get But, Substituting the above values in equation (ii), we get Rearranging the above equation we get But So the above equation becomes, But from sine rule, So the above equation becomes, Hence proved 6. Question In any triangle ABC, prove the following: AnswerRead More
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Document Description: RD Sharma Solutions Commerce Maths Class 11 Class 11 Solutions Chapter - Sine for Commerce 2026 is part of Mathematics (Maths) Class 11 preparation. The notes and questions for RD Sharma Solutions Commerce Maths Class 11 Class 11 Solutions Chapter - Sine have been prepared according to the Commerce exam syllabus. Information about RD Sharma Solutions Commerce Maths Class 11 Class 11 Solutions Chapter - Sine covers topics like and RD Sharma Solutions Commerce Maths Class 11 Class 11 Solutions Chapter - Sine Example, for Commerce 2026 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for RD Sharma Solutions Commerce Maths Class 11 Class 11 Solutions Chapter - Sine.
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