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For two towers of height $h 1 a n d h 2; h 1 x = tan 60 ° a n d h 2 x = tan 30 °,$ at mid points of line joining their feet then $h 1 : h 2 =$ ?

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1:1

1:3

3:1

2:1

answer is B.

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Detailed Solution

The given equations are

h 1 x = tan 60 °

and

h 2 x = tan 30 °

which gives

h 1 = x tan 60 °

and

h 2 = x tan 30 °

.
We know,

\tan 60 ° = \sqrt{3}

\tan 30 ° = \frac{1}{\sqrt{3}}

Dividing both the equations,

h 1 h 2 = x tan 60 ° x tan 30 ° ⇒ h 1 h 2 = 313 ⇒ h 1 h 2 = 3 × 3 1 ⇒ h 1 h 2 = 31

Therefore,

h_{1} : h_{2} = 3 : 1 .

If at the mid-point of the distance between two towers of height

h 1

and

h 2

h 1 x = tan 60 ° and h 2 x = tan 30 °

, then

h_{1} : h_{2} = 3 : 1 .

Therefore, option 2 is correct.

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