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asked Dec 22, 2023 13.1k views

1 Answer

Cruz · Answer 1 · 2023-12-27T13:50:10+0000

Let
x,y be the legs of the triangle, with
$x[tex]\mathrm{area}_(\rm square) = y^2$

$\mathrm{area}_(\rm triangle) = \frac12 xy$

The square has 3 times the area of the triangle, so

$y^2 = \frac32 xy$

Meanwhile, in the triangle we have

$\tan(\theta) = \frac xy$

Now,

$y^2 = \frac32 xy \implies \frac23 = \frac xy \implies \boxed{\tan(\theta) = \frac23}$