QJEEM23Mab0e5: JEE Main 2023 Mathematics - Class 12 JEEM23Mab0e5 Solution: The angle of elevation of the top of a tower from the feet of…

Let's denote the person standing due south as S and the one standing due west as W. Also, let the tower be at point T.

From person S's perspective, we have a right triangle $\triangle SPT$ . The height of the tower PT is given as 5m, which is the opposite side for angle S. The angle at S is $45^\circ$ . From the tangent trigonometric ratio, we have :

$\tan{45^\circ} = \frac{PT}{ST} = \frac{5}{ST}$

Since $\tan{45^\circ}=1$ , we get $ST = 5$ m.

Similarly, from person W's perspective, we have a right triangle $\triangle WPT$ . The angle at W is $30^\circ$ . From the tangent trigonometric ratio, we have:

$\tan{30^\circ} = \frac{PT}{WT} = \frac{5}{WT}$

Since $\tan{30^\circ}=\frac{1}{\sqrt{3}}$ , we get $WT = 5\sqrt{3}$ m.

Since S and W are perpendicular to each other (one is due south and the other is due west), $\triangle SWT$ forms a right triangle.

We can find $SW$ (the distance between the two people) using the Pythagorean theorem:

$SW^2 = ST^2 + WT^2 = 5^2 + (5\sqrt{3})^2 = 25 + 75 = 100$

So, $SW = \sqrt{100} = 10$ m.

Hence, the correct answer is 10 meters, which corresponds to Option A.