Question

Sonia observes a person standing on the ground from the terrace of her house at an angle of depression ${45}^{\circ }$. The height of terrace from the ground is 500 m. What is the distance of person from Sonia.

• A. $300\sqrt{2}m$
• B. $400\sqrt{3}m$
• C. $500\sqrt{2}m$
• D. $400\sqrt{2}m$

Answer 1

The correct option is C $500\sqrt{2}m$

Let B be the base of the house and A be the point from where Sonia is observing the person and C be the point where the person is.

In ΔABC, AB = 500 m
$tan{45}^o=\frac{AB}{AC}$
$\Rightarrow 1=\frac{AB}{AC}$ $[\because tan{45}^o=1]$
⇒ AC = 500 m
Since, ΔABC is right angled at A.
So, $A{B}^2+A{C}^2=B{C}^2$
$\Rightarrow B{C}^2=(500{)}^2+(500{)}^2$
$\Rightarrow (BC{)}^2=2(500{)}^2$
$\therefore BC=500\sqrt{2}m.$
Distance between them is $500\sqrt{2}m$.

So, c is the correct option.