Question

A vertical pole $\mathrm{PO}$ is standing at the center of a square $\mathrm{ABCD}$. If $\mathrm{AC}$ subtends an $\angle 90°$ at the top $\mathrm{P}$ of the pole, then the angle subtended by a side of the square at is

• A. $30°$
• B. $45°$
• C. $60°$
• D. None of these

Answer 1

The correct option is C

$60°$

Finding the angle subtended by a side of the square at :

Given,

A vertical pole $\mathrm{PO}$ is standing at the center of a square $\mathrm{ABCD}$. If $\mathrm{AC}$ subtends an $\angle 90°$ at the top $\mathrm{P}$ of the pole.

$\angle OPA=\angle OPC=\frac{\mathrm{\pi }}{4}$

Let

$\Rightarrow \mathrm{OP}=\mathrm{n}$,

$\Rightarrow OA=n$

$\Rightarrow AC=2n$

Then,
$\Rightarrow PA=\sqrt{2}n$

$\Rightarrow \mathrm{AB}=\sqrt{2}\mathrm{n}$

Since, $\mathrm{PA}=\mathrm{PB}=\mathrm{AB}$

Therefore $△\mathrm{BPA}$ is an equilateral triangle $=60°$

Hence, correct option is $\mathbf{\left(}\mathit{C}\mathbf{\right)}$.