In the triangle ABC, it is known that AB = 4, AC = 7 and BC = √93. Find the radius of the circle circumscribed
| May 16, 2021 | education
In the triangle ABC, it is known that AB = 4, AC = 7 and BC = √93. Find the radius of the circle circumscribed about this triangle.
By the cosine theorem, we determine the value of the angle BAC.
BC ^ 2 = AB ^ 2 + AC ^ 2 – 2 * AB * AC * CosA.
93 = 16 + 49 – 2 * 4 * 7 * CosA.
56 * CosA = -28.
CosA = -1 / 2.
Angle BAC = 120.
Determine the radius of the circle circumscribed around the triangle.
R = (√93 / 2 * Sin120) = (√93 / (2 * √3 / 2) = √31
R = √31 cm.
Answer: The radius of the circumscribed circle is √31 cm.
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