Q) The angle of elevation of the top of a tower 30 m high from the foot of another tower in the same plane is 600 and the angle of elevation of the top of the second tower from the foot of the first tower is 300. Find the distance between the two towers and also the height of the other tower.
Let AB and PQ be the towers, heights be 30 m & H m; distance between 2 towers be D m, and angle of elevations be as shown in the image above.
In Δ ABQ,
or D = 10√3 m
Now in Δ PQB,
or H = 10 m
Therefore, the distance between the two towers is 10√3 m and the height of the other tower is 10 m.