The height BM, drawn from the vertex of the corner of the rhombus ABCD, forms an angle of 30 °

| March 17, 2021 | education

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

1. In a right-angled triangle ABM, the AM leg is opposite an angle of 30 °.

Therefore, its length, according to the properties of a right-angled triangle, is half the hypotenuse. The hypotenuse in this triangle is the AB side. AB = 2 x AM = 2 x 4 = 8 centimeters.

2. All sides of the rhombus are equal. Therefore, AB = AD = 8 centimeters. That is, the AED triangle is isosceles.

3. Calculate the degree measure ∠BAM:

∠BAM = 180 ° – (90 ° + 30 °) = 60 °.

4.∠АВD = ∠АDВ = (180 ° – 60 °) / 2 = 60 °.

All angles of triangle ABD are equal. Therefore, the indicated triangle is equilateral.

BD = AB = AD = 8 centimeters.

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



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.