Find the large diagonal of a rhombus whose side is 11√3 and the acute angle is 60 °.

| April 20, 2021 | education

1. Draw two diagonals in the rhombus.

Consider one of the 4 resulting triangles.

We know that the diagonals of a rhombus are the bisectors of its corners and at the point of intersection they are perpendicular and are divided in half.

Consider one of the 4 obtained triangles, which is formed by a side and half of the diagonals – the hypotenuse is half of the larger diagonal D, the angle between the side of the rhombus and half of the diagonal is 60 °: 2 = 30 °.

Using the trigonometry formula

Cos 30 ° is equal to the ratio of 1/2 D to the 11√3 side of the rhombus.

Find cos 30 ° = √3 / 2 from the table.

We can find 1/2 D:

1/2 D = √3 / 2 * 11√3 = 11 * 3/2 = 16 1/2 = 16.5.

Calculate the large diagonal D = 2 * 16.5 = 33

Answer: The large diagonal of the rhombus is 33.



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