16. The angles of elevation of the top of a tower from two points at a distance of 4 m and
9 m from the base of the tower and in the same straight line with it are complementary.
Prove that the height of the tower is 6 m.
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The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. Prove that the height of the tower is 6 m.ANSWER
∠C and ∠D are complementary .....given
In △ABC,
BC
AB
=tanQ ...(i)
In △ABD,
BD
AB
=tan(90−Q)
9
AB
=cotQ ...(ii)
9
AB
=
tanQ
1
andtanQ=
AB
7
Put value of tanQ in eqn (ii)
∴
BC
AB
=
AB
9
AB
2
=9BC
AB=
36
=6
Height of tower =6m
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