In an isosceles triangle with a side equal to 18 cm, the angle at the top of the tee is 120 °
| June 25, 2021 | education
In an isosceles triangle with a side equal to 18 cm, the angle at the top of the tee is 120 °. Find the radius of the circle circumscribed about this triangle.
By the cosine theorem, we define the length of the AC side.
AC ^ 2 = AB ^ 2 + BC ^ 2 – 2 * AB * BC * Cos120 = 324 + 324 + 324 = 972.
AC = 18 * √3 cm.
Then AH = AC / 2 = 9 * √3 cm.
In a right-angled triangle ABH, according to the Pythagorean theorem, we define the length of the leg BH.
BH ^ 2 = AB ^ 2 – AH ^ 2 = 324 – 81.
BH = 9 cm.
Determine the area of the triangle ABC.
Sас = АС * ВС / 2 = 18 * √3 * 9/2 = 81 * √3 cm2.
Determine the radius of the circumscribed circle.
R = AB * BC * AC / 4 * Savs = 18 * 18 * 18 * √3 / 4 * 81 * √3 = 18 cm.
Answer: The radius of the circumscribed circle is 18 cm
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