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

 

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