The smaller side AB of the rectangle ABCE is 5 cm, the diagonals AC and BE intersect

| August 9, 2021 | education

The smaller side AB of the rectangle ABCE is 5 cm, the diagonals AC and BE intersect at an angle of 60 degrees. Find the lengths of the diagonals AC and BE.

The diagonals of a rectangle always form 4 isosceles triangles with apex at the intersection of the diagonals, and the opposite triangles are the same. The sum of all angles in any triangle is 180 °. In an isosceles triangle, the angles opposite to the apex are equal. If the angle at the vertex is 60 °, then the sum of the other two angles is 180 – 60 = 120, and since the sought angles are equal, each of them is also 60 °. If in a triangle all angles are equal and equal 60 °, then this triangle is equilateral. Since one side is known and equal to 5 cm, therefore, all sides of the triangle are 5 cm. These sides are halves of the diagonals of the rectangle. It turns out that each diagonal is 5 + 5 = 10 cm.



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