JEE Main 2023 — Heights and Distances Question with Solution

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 $x_1,x_2$.
$\Rightarrow \tan {45}^{°}=\frac{5}{x_1}, \tan {30}^{°}=\frac{5}{x_2}$
$\Rightarrow x_1=5, x_2=5\sqrt{3}$.

$\Rightarrow AB=\sqrt{{x_1}^2+{x_2}^2}=\sqrt{{\left(5\right)}^2+{\left(5\sqrt{3}\right)}^2}=10 m$

Hence this is the correct option.