In triangle ABC, AB = 10cm, BC = 7cm and angle BAC = 40° (a) Find, in degrees to the nearest 0.1°, the two possible sizes of angle ACB.
(b) Find, in cm to 3 significant figures, the difference between the two possible lengths of AC.
I came across this when looking through the edexcel further pure maths past papers I got question (a) pretty easily, i also got question(b) using the cosine rule,and the answer is also correct but When i read through the mark scheme the solution given is by drawing a isosceles triangle BCC', then finding half of the base length CC"=7cos 66.67° and doubling CC'. How does this method works?I cannot seem to understand it.
Here is the link to the mark scheme. The question number is 5. https://qualifications.pearson.com/content/dam/pdf/International%20GCSE/Further%20Pure%20Mathematics/2009/Exam%20materials/4PM0_01_rms_20170823.pdf