Question

Read the following paragraph and answer the questions.
The angle of elevation of a tower of height h 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 persons is

• A. $hcot\alpha$
• B. $cot\beta$
• C. $h(cot\alpha +cot\beta )$
• D. $h(cot\beta -cot\alpha )$

Answer 1

The correct option is D

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

To find AB
In $\Delta CDA$
$tan\alpha =\frac{h}{x}\Rightarrow x=hcot\alpha$ ....(i)
In $\Delta CDB$,
$tan\beta =\frac{h}{y}\Rightarrow y=hcot\beta$ ....(ii)
Now, AB=y-x
$=hcot\beta -hcot\alpha =h(cot\beta -cot\alpha )$
[from Eqs. (i) and (ii)]