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Question:

The angles of elevation of the top of a tower from two points at a distance of 4m and 9m from the base of the tower and in the same straight line with it are complementary. Prove that the height of the tower is 6m.

Solution:

∠C and ∠D are complementary. given
In △ABC, AB/BC = tanQ.. (i)
In △ABD, AB/BD = tan(90−Q)
AB/9 = cotQ.. (ii)
AB/9 = 1/tanQ
and tanQ = 9/AB
Put value of tanQ in eqn (ii)
∴ AB/BC = 9/AB
AB² = 9BC
AB = √36 = 6
Height of tower = 6m