Question

From a window 20 metres high above the ground in a street, the angle of elevation and depression of the top and the foot of another house on the opposite side of the street are 45º and 30º respectively. The height of the opposite house is $[\sqrt{3}=1.732]$

• A.
  54.64 m
• B.
  54.46 m
• C.
  56.44 m
• D.
  34.64 m

Answer 1

The correct option is A

54.64 m
Let AB be the window 20 m high above the ground in a street and CD be the house of height h.
$In\Delta BED,$
$\tan {45}^{\circ }=\frac{DE}{BE}$
$\Rightarrow 1=\frac{DE}{BE}$
$\Rightarrow BE=DE=h-20$ ....(i)
$In\Delta BEC,$
$\tan {30}^{\circ }=\frac{EC}{BE}$
$\Rightarrow \frac{1}{\sqrt{3}}=\frac{20}{h-20}$ [From (i)]
$\Rightarrow h-20=20\sqrt{3}$
$\Rightarrow h=20(\sqrt{3}+1)m$
$\Rightarrow h=54.64m$
Hence, the correct answer is option (a).