Find the length of a circle inscribed in a rhombus with a side equal to 12 and an acute angle of 30 degrees.
| August 18, 2021 | education
Let’s build the height BH of the rhombus ABCD.
In a right-angled triangle ABH, by condition, the angle BАH = 30.
The BH leg lies opposite an angle of 30, then its length is equal to half the length of the AB hypotenuse.
BH = AB / 2 = 12/2 = 6 cm.
The diameter of the inscribed rhombus of the circle is equal to the length of the height of the rhombus, then R = BH / 2 = 6/2 = 3 cm.
Determine the length of the inscribed circle.
L = 2 * π * R = 6 * π see.
Answer: The length of the inscribed circle is 6 * π cm.
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.
