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Chapter 10: Sine and Cosine Formulae and Their Applications – Exercise 10.1

Sine and Cosine Formulae and Their Applications – Exercise 10.1 – Q.1

∠A = 45°,∠B = 60° and ∠C = 75°

Using sine rule,



 

Sine and Cosine Formulae and Their Applications – Exercise 10.1 – Q.2

∠C = 105°, ∠B = 45°, a = 2

From here we can calculate that

∠A = 30°

a sin B = b sin A

⟹ 2sin 45 = b sin 30



 

Sine and Cosine Formulae and Their Applications – Exercise 10.1 – Q.3

a = 18, b = 24, c = 30, ∠C = 90°



 

Sine and Cosine Formulae and Their Applications – Exercise 10.1 – Q.4




Let a = k sin A, b = k sin B (Using sine rule)

LHS




 

Sine and Cosine Formulae and Their Applications – Exercise 10.1 – Q.5



Let a = k sin A, B = k sin B, c = k sin C

LHS,



 

Sine and Cosine Formulae and Their Applications – Exercise 10.1 – Q.6



LHS,



= RHS

 

Sine and Cosine Formulae and Their Applications – Exercise 10.1 – Q.7



LHS,



= RHS

 

Sine and Cosine Formulae and Their Applications – Exercise 10.1 – Q.8



Let a = k sin A, b = k sin B, c = k sin C

LHS,



 

Sine and Cosine Formulae and Their Applications – Exercise 10.1 – Q.9




Let a = k sin A, b = k sin B, c = k sin C

RHS,



 

Sine and Cosine Formulae and Their Applications – Exercise 10.1 – Q.10



LHS,

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