A flagstaff stands on the top of a 5 m high tower. From a point on the ground, the angle of elevation of the top of the flagstaff is 60 0 and from the same point, the angle of elevation of the top of the tower is 45 0 . Find the height of the flagstaff.
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Answer:
Based on the given information, we can draw the figure shown above.
Let BC be the height of the tower and DC be the height of the flag-staff.
In right triangle ABC,
AB=BCcot45
o
AB=5 m .........(1)
In right triangle ABD,
AB=BDcot60
o
AB=(BC+CD)cot60
o
AB=(5+CD)
3
1
......(2)
Equating 1 and 2, we get,
(5+CD)
3
1
=5
CD=5
3
−5=5×0.732=3.66 m
Therefore, the height of the flagstaff is 3.66 m.