In an equilateral triangle ABC, the CH height is 39√3. Find the sides of this triangle.

univerkov | August 5, 2021 | education

The CH in an equilateral triangle is the height, bisector, and median.

<C = 60 °,

<ACH = 1/2 <C = 30 °; AH = HB = 1/2 AB = 1/2 AC; AC = 2 AH;

AC² = AH² + HC²; 4 AH² = AH² + 3 * 39²;

3 AH² = 3 * 39²; AH² = 39²; AH = 39;

AC = AB = DC = 2 * 39 = 78;

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