Two equilateral triangles ABC and ABD lie in perpendicular planes. Find the length of the segment CD

| March 5, 2021 | education

Two equilateral triangles ABC and ABD lie in perpendicular planes. Find the length of the segment CD if the side of the triangle is √6

By condition, triangles ABC and ABD are equilateral, having a common side, which means they are equal to each other. Consequently, the heights drawn from the corners C and D to the side AB are also equal. In an equilateral triangle, all angles are 60 degrees, any height of such a triangle can be found as the product of the side and the sine of the angle, which means the height drawn to AB is equal to √6 * sin60 = √6 * √3 / 2 = 3 / √2. The heights drawn from the corners C and D to the side AB, and the segment CD form a right-angled triangle, in which CD is the hypotenuse. The square of the hypotenuse is equal to the sum of the squares of the legs, CD ^ 2 = (3 / √2) ^ 2 + (3 / √2) ^ 2 = 9, CD = √9 = 3.



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