In a triangle ABC, AB = 3√2, AC = 4, the area of the triangle ABC = 6. Find: BC.

univerkov | November 22, 2020 | education

Based on the condition, we can find the sine of the angle A
sinA = S / AB * AC * 1/2
sinA = 1 / √2
Find the cosine of the angle
Cos ^ 2 = 1-sin ^ 2
cos ^ 2 = 1-1 / 2 = 1/2
cosA = 1 / √ 2
By the cosine theorem:
BC ^ 2 = AC ^ 2 + AB ^ 2-2 * AC * AB * cos A
BC ^ 2 = 10
BC = √10

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