Step-by-step explanation:
(i) Use law of cosine:
c² = a² + b² − 2ab cos C
c² = (√3 − 1)² + (√3 + 1)² − 2(√3 − 1)(√3 + 1) cos 60°
c² = 3 − 2√3 + 1 + 3 + 2√3 + 1 − 2(3 − 1) (½)
c² = 6
c = √6
(ii) Use law of sines:
a / sin A = c / sin C
(√3 − 1) / sin A = √6 / (½√3)
(√3 − 1) / sin A = 2√2
½ (√3 − 1) = √2 sin A
½ (√6 − √2) = 2 sin A
¼ (√6 − √2) = sin A
Use a calculator:
A = 15°
(iii) Use SAS area:
A = ½ ab sin C
A = ½ (√3 − 1) (√3 + 1) sin 60°
A = ½ (3 − 1) (½√3)
A = ½√3
