The diagonals of a rhombus are 12 and 16. Find the cosine of its obtuse angle.
| June 9, 2021 | education
The diagonals of the rhombus, at the point of their intersection, are halved and intersect at right angles.
Then AO = CO = 16/2 = 8 cm, BO = AO = BD / 2 = 12/2 = 6 cm, and the ABO triangle is rectangular.
By the Pythagorean theorem, we determine the length of the hypotenuse AB.
AB ^ 2 = AO ^ 2 + BO ^ 2 = 64 + 36 = 100.
AB = 10 cm.
AED triangle isosceles AB = BC = 10 cm.
By the cosine theorem, we define the cosine of the angle ABC.
AC ^ 2 = AB ^ 2 + BC ^ 2 – 2 * AB * Sun * CosABS.
256 = 100 + 100 – 200 * CosABS.
200 * CosABC = -256 + 200
CosABC = -56 / 200 = -0.28.
Answer: The cosine of an obtuse angle is -0.28.
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