When to use ‘Law of Cosines’ for triangle
CASE 2
QUESTION: Given ΔABC, with AB = 10cm, 𝐵C =6cm and ∠𝐵 =110°. What is the measure of AC?
SOLUTION:
Let AB = a = 10cm
BC = b = 6cm
∠B = 1100
c = ?
By Law of Cosines
c² = a² + b² – 2ab Cos B
Put values in the above formula
c² = (10)² +(6)² – 2(10)(6) Cos (110)
c² = 100 + 36 – 120 (-0.342)
c² = 177.042
Take square root on both sides
c = ± 13.3 cm
Since length is always positive
So, c = 13.3 cm
Thus, in ΔABC, if AB = 10cm, 𝐵C =6cm and ∠𝐵 =110° then the measure of AC is 13.3 cm
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