Question

If Karan stands at a point which is 2m from A and 4m from B, the angles of elevation of the top of the poles at points A and B are complimentary. What is the shortest distance between the topmost points of the poles, if the height of the pole at B is twice the height of the pole at A?

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

$\angle ACD+\angle BCE={90}^{\circ }In\Delta ADCtan\angle ACD=\frac{AD}{AC}....\left(i\right)In\Delta BCEtan({90}^{\circ }-\angle ACD)=\frac{BE}{BC}....\left(ii\right)$
Multiplying (i) and (ii) we get
$AD\times BE=AC\times BC$
Let AD = h m
BE = 2h m
$2h^2=8$
h = 2
Using Pythagoras theorem in $\Delta$ ADC and $\Delta$ BEC we get
$DC=2\sqrt{2}m$
$EC=4\sqrt{2}m$
Join DE
$\angle DEC={90}^{\circ }$ (Sum of angles on a straight line is ${180}^{\circ }$)
Using Pythagoras theorem in $\Delta$ DEC
$D{E}^2=D{C}^2+C{E}^2$
$DE=2\sqrt{10}m$