In equilateral triangle ABC, point O is the intersection of the heights drawn from the vertices to the bases. Determine the angle between the heights of the triangle.
Since ABC is an equilateral triangle, its angles are 60˚. The heights drawn from the vertices are also bisectors that divide the angle in half: 60˚ / 2 = 30˚.
This means: angle BAO = angle ABO = 30˚.
Find the angle AOB.
Angle AOB = 180˚ – 30˚ – 30˚ = 120˚.
Answer: the angle between the heights of the triangle is 120˚.
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