Question

The angle of elevation of a tower of height m from the eye of two observers A and B on the same side of the tower are $\alpha$ and $\beta$. respectively. If the distance between the foot of the tower and the person nearer to tower is x and the distance between the tower and second person is y. Then,
The distance between the two people is :

• A. $bcot\alpha$
• B. $cot\beta$
• C. $b(cot\alpha +cot\beta )$
• D. $b(cot\beta -cot\alpha )$

Answer 1

The correct option is D

$b(cot\beta -cot\alpha )$

To find AB
In $\Delta CDA$
$tan\alpha =\frac{b}{x}\Rightarrow x=b\cot \alpha$ ....(i)
In $\Delta CDB$,
$tan\beta =\frac{b}{y}\Rightarrow y=bcot\beta$ ....(ii)
Now, AB=y-x
$=b\cot \beta -b\cot \alpha =b(\cot \beta -\cot \alpha )$