A circle is circumscribed about a triangle. If one of the angles of the triangle is 120°, and the radius of the circumscribed circle is r, what is the length of the side opposite the 120° angle?
\(r\sqrt{3}\)
For a triangle with circumradius \(R\), the Law of Sines (extended form) states:
\(\dfrac{a}{\sin A} = 2R\)
where \(a\) is the side opposite angle \(A\).
Apply with \(A = 120^{\circ},\ R = r\):
\(a = 2r \cdot \sin 120^{\circ}\)
Use \(\sin 120^{\circ} = \dfrac{\sqrt{3}}{2}\):
\(a = 2r \cdot \dfrac{\sqrt{3}}{2} = r\sqrt{3}\)
Hence, the answer is option A.
Similar Questions
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A triangle can have:
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Important Questions from Triangles, Congruence and Similarity
G is the centroid of the equilateral triangle ABC. If AB = 8√ 3 cm, then the length of AG is equal to:
If sides of a triangle are 12 cm, 15 cm and 21 cm, then what is the inradius (in cm) of the triangle?
What is the area of quadrilateral ABCD?
It is given that ΔABC ~ ΔXYZ and Area ΔABC : Area ΔXYZ = 81 : 25. If AB = 18 cm, BC = 10 cm, CA = 15 cm, then what is the side XZ (in cm)?
Sides of two similar triangles are in the ratio 4 ∶ 9. Area of these triangles are in the ratio:
