NTA Abhyas JEE Main2020MathematicsHeights and DistancesPractice
A vertical tower subtends an angle of 60 o at a point on the same level as the foot of the tower. On moving 100   m further from the first point in line with the tower, it subtends an angle of 30 o at the point. If the height of the tower is H   m , then the value of H 25 3 (in meters) is
Correct answer
2
Step-by-step solution
tan ⁡ 60 o = H x ,   tan ⁡ 30 o = H x + 100 ⇒ H t a n 6 0 ∘ = H t a n 3 0 ∘ - 100 ⇒ H 3 = H 1 3 - 100 ⇒ 3 H - H 3 = 100 ⇒ 3 H - H = 100 3 ⇒ H = 50 3 H 25 3 = 2