RD Chapter 10 Sine and Cosine Formulae and Their Applications Ex 10.1 Solutions
Question - 1 : - If in a∆ABC, ∠A = 45o, ∠B = 60o,and ∠C = 75o; findthe ratio of its sides.
Answer - 1 : -
Given: In ∆ABC, ∠A = 45o, ∠B = 60o,and ∠C =75o
By using the sine rule, we get
a: b: c = 2: √6: (1+√3)
Hence the ratio of the sides of the given triangle isa: b: c = 2: √6: (1+√3)
Question - 2 : - If in any ∆ABC, ∠C = 105o, ∠B = 45o, a = 2, then find b.
Answer - 2 : -
Given: In ∆ABC, ∠C = 105o, ∠B = 45o, a =2
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°
By using the sine rule, we get
Question - 3 : - In ∆ABC, if a = 18, b = 24 and c = 30 and ∠C = 90o, find sin A, sin B and sin C.
Answer - 3 : -
Given: In ∆ABC, a = 18, b = 24 and c = 30 and ∠C = 90o
By using the sine rule, we get
In anytriangle ABC, prove the following:
Question - 4 : - 
Answer - 4 : -
By using the sine rule we know,
= RHS
Hence proved.
Question - 5 : - (a – b) cos C/2 = C sin (A – B)/2
Answer - 5 : - By using the sine rule we know,
Question - 6 : - 
Answer - 6 : - By using the sine rule we know,
Question - 7 : - 
Answer - 7 : - By using the sine rule we know,
cos (A + B)/2 = cos (A/2 + B/2) = cos A/2 cos B/2 +sin A/2 sin B/2
cos (A – B)/2 = cos (A/2 – B/2) = cos A/2 cos B/2 –sin A/2 sin B/2
Substituting the above equations in equation (vi) weget,
Answer - 8 : - By using the sine rule we know,
Question - 9 : - 
Answer - 9 : -
Question - 10 : - 
Answer - 10 : -