The side of a regular pentagon is 2 cm, calculate the diagonal of the pentagon.
| September 4, 2021 | education
Let us define the degree measure of the arcs into which the pentagon divides the circle.
Arc BC = 360/5 = 720.
Then the central angle BOC = 720.
The triangle BОС is isosceles, then the angle ОСB = (180 – 72) / 2 = 540.
The triangles BОС and СОD are equal on three sides, then the angle BОС = 2 * OCB = 2 * 54 = 108.
In the triangle BCD, according to the cosine theorem, BD ^ 2 = BC ^ 2 + CD ^ 2 – 2 * BC * CD * Cos108 = 4 + 4 – 2 * 2 * 2 * (-0.31) = 10.48 cm.
BD = 3.237 cm.
Answer: The diagonal of the pentagon is BD = 3.237 cm.
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