Question

2. 7 cm In triangle ABC, AC = 7 cm, BC = 10 cm, angle ACB = 73° C 73° 10 cm Calculate the length of AB Give your answer correct to 3 significant figures. Diagram NOT accurately drawn B (Total 3 marks​

Answer 1

AB = 10.398

Explanation:

By cosine rule, we have:

AB² = AC² + BC² - 2(AC)(BC)cos(ACB)

⇒ AB² = 7² + 10² - 2(7)(10)cos(73)

⇒ AB² = 49 + 100 - 140cos(73)

⇒ AB² = 149 - 140cos(73)

⇒ AB² = 149 - 140cos(73)

⇒ AB² = 149 - 140(0.292)

⇒ AB² = 149 - 40.88

⇒ AB² = 108.12

⇒ AB = √(108.12)

⇒ AB = 10.398