Question

A fire is reported in a building .there are two fire stations on either side of the building and the straight line with it.the elevation of the building from the station a and bare 30degree and 60 degree respectively. which fire station is closer to building

Answer 1

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Answer 2

Answer:  Fire station B is closer to building.

Step-by-step explanation:

Since we have given that

There are 2 fire station on either side of the building and the straight line with it.

The angle of elevation of the building from the station A and B are 30 degree and 60 degree respectively.

So, we need to find the fire station which is closer to building.

As we know that " Larger the angle nearer the object ".

So, now we will prove it.

As shown in the figure:

Consider, ΔCAD,

$\tan 30^\circ=\frac{CD}{AD}\\\\\frac{1}{\sqrt{3}}=\frac{h}{AD}\\\\AD=h\sqrt{3}$

Consider, ΔCDB ,

$\tan 60^\circ=\frac{CD}{DB}\\\\\sqrt{3}=\frac{h}{DB}\\\\DB=\frac{h}{\sqrt{3}}$

And we know that, $\frac{h}{\sqrt{3}}<h\sqrt{}3$

Hence, Fire station B is closer to building.