Each side of a square subtends an angle of 60 ° at the top of a...

Let, $ABCD$ be a square with each side of length $a .$

It is given that $∠BPC = 60 °$
Let, $M$ be the midpoint of $BC .$

Then, $∠BPM = ∠CPM = 30 °$

In $∆ BMP,$ right angled at $M,$
we have, $\tan \left(∠BPM\right) = \dfrac{BM}{PM}$
In $∆ OPM$
$\dfrac{3{a}^{2}}{4}=\dfrac{{a}^{2}}{4} + {5}^{2}$
$∴ {a}^{2} = 50 ⇒ a = 5\sqrt{2}m$