# The height BM, drawn from the vertex of the rhombus angle ABCD, forms an angle of 30 degrees with the side AB

September 30, 2021 | education

| **The height BM, drawn from the vertex of the rhombus angle ABCD, forms an angle of 30 degrees with the side AB, AM = 4cm. Find the length of the diagonal BD of the rhombus if the point M lies on the side of AD.**

Since BM is the height of a rhombus, the ABM triangle is rectangular, in which the ABM angle, by condition, is 30.

Then the angle BAM = (90 – 30) = 60.

Since all the faces of a rhombus are equal, then AB = AD, and then the triangle ABD is isosceles, and since the angle BAD = 60, then the triangle ABD is equilateral.

Then the height of the BM is also the median of the triangle ABD, then AM = DM = 4 cm, AD = BD = 8 cm.

Answer: The length of the diagonal BD is 8 cm.

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