Question

From the top of a tower 100 m high, a man observes two cars on the opposite sides of the tower and in same straight line with its base, with angle of depression ${30}^0$ and ${45}^0$ respectively. Find the distance between the cars.$(Take\sqrt{3}=1.732)$

Answer 1

Height ot tower $=Co=100m$

Let $A$ and $B$ are the points for two cars.

So distance between them is $AB$

As $AB=AO+OB$

Now in $△AOC$

$\tan {30}^o=\frac{OC}{AO}$

$\frac{1}{\sqrt{3}}=\frac{100}{AO}$

$AO=100\sqrt{3}m$

Similarly in $△BOC$

$\tan {45}^o=\frac{OC}{OB}$

$1=\frac{100}{OB}$

$OB=100m$

Now $AO+OB=AB$

So $AB=100\sqrt{3}+100$

$=100(\sqrt{3}+1)$

$=100(1.732+1)$

$AB=273.2m$