Each side of a square subtends an angle of 60 ° at the top of a tower 5 meters high standing at the center of the square. If a meters is the length of each side of the square, then a is equal to ( use 2 = 1 .41 )

Step-by-step solution

Let, A B C D be a square with each side of length a . It is given that ∠ B P C = 60 ° Let, M be the midpoint of B C . Then, ∠ B P M = ∠ C P M = 30 ° In ∆ B M P , right angled at M , we have, tan ⁡ ∠ B P M = B M P M In ∆ O P M 3 a 2 4 = a 2 4 + 5 2 ∴ a 2 = 50 ⇒ a = 5 2 m