Each side of a square subtends an angle of 60° at the tip of a tower of height h meters standing at the centre of the square. If l is the length of each side of the square, then what is h2equal to?a)2l2b)l2/2c)3l2/2d)2l3/3Correct answer is option 'B'. Can you explain this answer?

Question

Each side of a square subtends an angle of 60&deg; at the tip of a tower of height h meters standing at the centre of the square. If l is the length of each side of the square, then what is h2equal to?a)2l2b)l2/2c)3l2/2d)2l3/3Correct answer is option 'B'. Can you explain this answer?

Answer

Given Data:
- Each side of a square subtends an angle of 60° at the tip of a tower of height h meters standing at the center of the square.
- Length of each side of the square = l meters

To Find:
h² in terms of l

Solution:

Step 1: Find the diagonal of the square
- The diagonal of the square can be calculated using the formula:
Diagonal² = Side² + Side²
Diagonal² = 2l²
Diagonal = √(2l²) = l√2

Step 2: Find the distance from the center of the square to one of its vertices
- The tower stands at the center of the square. Therefore, the distance from the center to one of the vertices is half the diagonal of the square.
Distance = l√2 / 2 = l/√2

Step 3: Find the height of the tower h
- In a right-angled triangle with the tower height as the opposite side, distance as the adjacent side, and hypotenuse as h, we can use trigonometric ratios.
tan(60°) = h / (l/√2)
√3 = h / (l/√2)
h = l/2√3

Step 4: Find h² in terms of l
h² = (l/2√3)²
h² = l² / (4*3)
h² = l² / 12
Therefore, h² = l² / 12, which is equivalent to h² = l² / 2.

Therefore, the correct answer is option B) l²/2.

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