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Question

A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff. At a point on the plane, 30 metres away from the tower, an observe notices that the angles of elevation of the top and bottom of the flagstaff are 60° and 45° respectively. Find the height of the flagstaff and that of the tower.

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Solution

Let OX be the horizontal line, AC be the vertical tower and BC be the vertical flagstaff.
We now have:
OA = 30 m, ∠BOA = 60o and ∠COA = 45o
Let:
AC= h m and BC = x m



In the right ∆AOC, we have:
ACOA = tan 45o = 1

h30 = 1
h = 30 m

Now, in the right ∆AOB, we have:
ABOA = tan 60o = 3

h + x30 = 3
On putting h = 30 in the above equation, we get:
30 + x = 303
x = 303 - 30 = 21.96 m

We now have:
Height of the flagstaff = x = 21.96 m
Height of the tower = h = 30 m

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