The height BM, drawn from the apex of the rhombus angle ABCD, forms an angle of 30 degrees with side AB
| September 12, 2021 | education
The height BM, drawn from the apex of the rhombus angle ABCD, forms an angle of 30 degrees with side AB, the length of the diagonal AC = 6 cm. Find AM if point M lies on the continuation of side AD.
Triangle ABM is rectangular, angle BAM = 90 – 30 = 60.
The angle BAD is adjacent to the angle BAM, then BAD = 180 – 60 = 120.
The diagonal AC is the bisector of the angle BAD, then the angle BAC = 120/2 = 60, then the triangle ABC is equilateral, since AB = BC as the sides of the rhombus.
AB = AC = 6 cm.
In a right-angled triangle ABM, the AM leg lies opposite an angle of 30, then AM = AB / 2 = 6/2 = 3 cm.
Answer: The length of the segment AM is 3 cm.
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