2018 · Q58
Each side of a square subtends an angle of 60° at the tip of a tower of height h metres standing at the centre of the square. If l is the length of each side of the square, then what is h² equal to?
Elementary MathematicsTrigonometry
- A2l²
- Bl²/2
- C3l²/2
- D2l²/3
Explanation
The tip T and any side form an equilateral triangle (TA = TB with included angle 60°), so side l equals the slant edge √(h² + (l√2/2)²). Hence l² = h² + l²/2, giving h² = l²/2, option (B).