The angle of elevation of the top of a tower from point S is 30°. If the observer moves 10 meters towards the tower which is point T, the angle of elevation of the top increases by 15°. What will be the height of the tower?

Let the height of the tower = h m. Point T Angle = 45, distance = x m ➩ tan 45 = h / x ➩ 1 = h / x ➩ x = h Point S Angle = 30, distance = x + 10 m ➩ tan 30 = h / (x + 10) ➩ 1 / √3 = h / (h + 10) ➩ h + 10 = h√3 ➩ 10 = h√3 – 1 ➩ 10 = h (√3 – 1) ➩ h = 10 / (√3 – 1)