The side of the rhombus is 12 and the acute angle is 60 degrees. The height of the rhombus

| May 5, 2021 | education

The side of the rhombus is 12 and the acute angle is 60 degrees. The height of the rhombus, dropped from the vertices of the obtuse angle, divides the side into 2 segments. How long are these segments?

1. The vertices of the rhombus A, B, C, D. ∠A = 60 °. VN – height.

We calculate the length of the height of the ВН through the sine ∠A of the right-angled triangle ABН.

Sine 60 ° = √3 / 2.

Sine ∠A is the ratio of the length of the height BH, which in the indicated triangle is the leg opposite this angle, to the hypotenuse AB.

BH / AB = √3 / 2.

BH = AB x √3 / 2 = 12 x √3 / 2 = 6√3 units.

2. Calculate the length of the segment AH using the Pythagorean theorem:

AH = √AB² – BH² = √12² – (6√3) ² = √144- 108 = 6 units.

3. Calculate the length of the segment DH:

12 – 6 = 6 units.

Answer: the height BH divides the side of the rhombus AD into two identical segments AH = DH = 6 units of measurement.



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