Height and Distance: JEE Main 2019 Mathematics question

ABC is a triangular park with AB = AC = 100 metres. A vertical tower is situated at the mid-point of BC. If the angles of elevation of the top of the tower at A and B are cot^–1 (3$\sqrt 2$ ) and cosec^–1 (2$\sqrt 2$ ) respectively, then the height of the tower (in metres) is :