Math mini-contest trigonometry problem for Day 4 on D.Buzz for May 2021 😎

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Math mini-contest problem for Day 4 on D.Buzz for May 2021 😎

Vision knew that the value of tan (2A), where A is one of the acute angles of a right triangle with integer sides, has a value of approximately 1.0084. What is the minimum possible area of the triangle?

math mathematics dbuzz minicontest contest trigonometry
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tan(2A) = 1.0084 <=> 2A = arctan(1.0084)
=> A = 0.3948
tan(A) = 0.41666 == opposite / adjacent
the smallest integers for opposite and adjacent would be 5 and 12: 5/12 = 0.41666
=> area = 1/2 * opposite * adjacent = 30

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