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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.1

 

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.2

 

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.3

 

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

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.4(i)

 

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

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.5(i)

 

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

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

LHS,

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

= RHS

 

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

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

LHS,

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

= RHS

 

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

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.8(i)

 

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

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.9(i)

 

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

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

LHS,

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


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