A person walking on a straight horizontal road towards a vertical tower observes the angle of elevation of the top of the tower to be 15^ . After walking a distance of 80 m towards the tower, the angle of elevation of the top of the tower becomes 30^ . The height of the tower (in m) is:

Step-by-step solution

Let the height of the tower be h and the final distance from the foot of the tower be x . From the second observation point, the angle of elevation is 30^ : 30^ = h x x = h 3 From the first observation point, the angle of elevation is 15^ and the distance is x + 80 : 15^ = h x + 80 We know that 15^ = 2 - 3 . Substituting x = h 3 into the equation: 2 - 3 = h h 3 + 80 Cross-multiplying gives: (2 - 3 )(h 3 + 80) = h 2h 3 - 3h + 160 - 80 3 = h 2h 3 - 4h = 80 3 - 160 -2h(2 - 3 ) = -80(2 - 3 ) Dividing both sides by -2(2