Math mini-contest trigonometry problem for Day 5 on D.Buzz for May 2021 😎

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Math mini-contest problem for Day 5 on D.Buzz for May 2021 😎

For a triangle DEF whose height is FG and G is on side DE, Manga got arctan (FG/DG) β‰ˆ 1.176, while Minos got arctan (FG/GE) β‰ˆ 0.330. What is the minimum possible area of the triangle if FG is an integer?

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  1. Area = 1/2 DG * FG + 1/2 GE * FG = 1/2 FG ( DG + GE)
  2. FG/DG = tan(1.126) = 2.0979
  3. FG/GE = tan(0.330) = 0.3425

The smallest integer for FG is 1 (excluding 0, since otherwise all other values are useless)
setting FG=1 in 2) and 3) to solve for DG and GE, then adding those into 1) gives
Area = 1/2*(1/2.0970 + 1/0.3425) = 1.698
can this be right?!

Wow, I used to easily solve these back on School... Now they require too much thinking.

I know the first step it to FG but I got lost. #MyBrainNeedsSugar

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Creating a Math problem that has (at least one) answer is (at least) twice as difficult as answering it. πŸ˜…

Yeah, I know. (My mother is a math teacher and used to say the same thing.) I commend you for all the effort you put on this!

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