SOLUTION: What is angle CAB using the cosine rule when AB = 12cm, AC = 16 cm and BC = 20 cm? Please show your working out.

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Question 729053: What is angle CAB using the cosine rule when AB = 12cm, AC = 16 cm and BC = 20 cm? Please show your working out.
Answer by Simnepi(216) About Me  (Show Source):
You can put this solution on YOUR website!
using the cosine rule is a waste of time!
if you draw the triangle, label it and examine the side lengths. They all can be divided by 4 giving a 3, 4, 5 triangle and is therefore a right angled triangle. so the angle CAB is 90 degrees.
HOWEVER if the cosine rule MUST be used........
the cosine rule is
a%5E2=b%5E2%2Bc%5E2-2bcCos%28A%29
rearranging gives
Cos%28A%29=%28b%5E2%2Bc%5E2-a%5E2%29%2F%282bc%29
substituting values gives us
Cos%28A%29=%284%5E2%2B3%5E2-5%5E2%29%2F%282%2A4%2A3%29
evaluating gives
cos%28A%29=%280%29%2F24
i.e. Cos(A)=0
therefore A = 90 degrees