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Can a scalene triangle be obtuse? Is an equilateral triangle always acute?

In the above diagram, \(\angle ABC=60^\circ\) and \(\angle ACB=60^\circ.\) If \(\lvert \overline{AB}\rvert =3,\) what is the area of \(\triangle ABC\)?

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In the above diagram, the side length of equilateral triangle \(\triangle ABC\) is \(a=3.\) If \(D\) is the midpoint of \(\overline{BC}\) and \(\triangle ADE\) is also an equilateral triangle, what is the area of \(\triangle ABE\)?

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In the above diagram, the triangle is the equilateral triangle. If \(\overline{AB}=5.\) What is the height of \(\triangle ABC\)?

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