The distance from the point of intersection of the diagonals of the rhombus to one of its sides is 19

| September 2, 2021 | education

The distance from the point of intersection of the diagonals of the rhombus to one of its sides is 19, and one of the diagonals of the rhombus is 76. Find the corners of the rhombus. In your answer, write down the angles in ascending order, separated by semicolons.

The diagonals of the rhombus, at the point of intersection, are divided in half and intersect at right angles, AO = AC / 2 = 76/2 = 38 cm, and triangle AOB is rectangular.

OK is the height of triangle AOB, then triangle OAK is rectangular.

In a right-angled triangle OAK, SinOAK = OK / AO = 19/38 = 1/2.

Then the angle OAK = 30.

The AC diagonal is the bisector of the BAD angle, then the BAD angle = 2 * 30 = 60.

The sum of the adjacent angles of the rhombus is 180, then the angle ABC = ADC = 180 – 60 = 120.

Answer: The angles of the rhombus are 60; 60; 120; 120.



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