The smaller side of the rectangle is 5 cm, the diagonals intersect at an angle of 60 °. Find the diagonal of the rectangle.
| September 23, 2021 | education
ABCD is a given rectangle.
Because the diagonals of the rectangle are equal and the intersection point is halved, then BO = AO.
The BOA triangle is isosceles.
∠ОВА = ∠ ОАВ = (180 ° – 60 °): 2 = 120 °: 2 = 60 °.
The BOA triangle is equilateral.
So ВO = AO = AB = 5 cm.
OС = AO = 5 cm.
AC = 5 + 5 = 10 (cm).
Answer: the diagonals of the rectangle are 10 cm.
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