MATH: The angles of depression of the top and bottom of a building 50m high as observed from the top of a tower are 30 and 45 respectively. Find the height of the tower and also the horizontal distance between the building and tower.
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Here CD is the tower and AB is the pole.
In △CDB, CD/BC = tan 60°
=> 50m/BC = √3
=> BC = 50/√3m
AE = BC
AE = 50/√3m
In △ADE, DE/AE = tan 45°
=> DE/50/√3m = 1
=> DE = 50/√3m
so the height of the pole is 50/√3m