Question

Question on the image​

Answer 1

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}`