Question

Each side of a square subtends an angle of 60 degree at the top of a tower h meters high standing in the centre of the square.If 'a' nis the length of each side of square, then prove that 3a^2 = 2h^2.

Answer 1

Keeping in view the attached image;

Since the sides of the square is a, the length of the diagonal is;

AC= √2a

So,

OA=AC/2

As, OB=h

In the triangle AOB,

tan60°=OB/OA

√3=h÷a/√2

√3a=√2h

When we square on both sides;

3a²=2h²