Each corner of a square subtends an angle of 30 $^{\circ}$ at the top of a tower 'h' meters high standing in the centre of the square. If 'a' is the length of the each side of square then the relation between h and a is

2a²= h²

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2h² = a²

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3a² =2h²

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2h² = 3a²

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Solution

The correct option is C
3a² =2h²

We can go ahead and assume values for H and deduce the value of a, substitute it in the given equations and eliminate the wrong answer choices.

Let us assume the value of h= $\sqrt{3}$

As it is a 30-60-90 triangle we will have the ratio as $1 : \sqrt{3} : 2$ .

Hence the diagonal of the square will be 2 and the side 'a' will be $\sqrt{2}$

Now applying this in the answer options we see that only option (c)gives us RHS= LHS.

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Each corner of a square subtends an angle of 30∘ at the top of a tower 'h' meters high standing in the centre of the square. If 'a' is the length of the each side of square then the relation between h and a is

Each corner of a square subtends an angle of 30 $^{\circ}$ at the top of a tower 'h' meters high standing in the centre of the square. If 'a' is the length of the each side of square then the relation between h and a is