The angle of elevation of the top P of a tower from the feet of one...

Given that the elevation to the top of the tower from the feet of one person due south is $= 45 °$

Similarly the angle of elevation to the top of tower from the feet of another person to the west of tower is $= 30 °$

The given information can be represented in the form of a diagram as below:

We need to find the distance $AB$.

Let the distance of $A, B$ from the tower be ${x}_{1}, {x}_{2}$.
$⇒ tan{45}^{°} = \dfrac{5}{{x}_{1}}, tan{30}^{°} = \dfrac{5}{{x}_{2}}$
$⇒ {x}_{1} = 5, {x}_{2} = 5\sqrt{3}$.

$⇒ AB = \sqrt{{{x}_{1}}^{2} + {{x}_{2}}^{2}} = \sqrt{{\left(5\right)}^{2} + {\left(5\sqrt{3}\right)}^{2}} = 10m$

Hence this is the correct option.