Question

A vertical tower stands on a horizontal plane and is surmounted by a

vertical flag staff of height 5m. At a point on the plane, the angles of

elevation of the bottom and the top of the flag staff are 45

and 60

,

respectively. Find the height of the flag staff.​

Answer 1

Answer:

Let AB be the tower of height h meter and BC be the height of flag staff surmounted on the tower. Let the point of the plane be D at a distance m meter from the foot of the tower.

In △ ABD,

tan30

∘

=

BD

AB

⇒

3

1

=

x

h

⇒x=

3

h.......(1)

In △ADC,tan60

∘

=

AD

AC

⇒

3

=

x

5+h

⇒x=

3

5+h

.....(2)

From (1) and (2),

3

h=

3

5+h

⇒3h=5+h⇒2h=5

⇒h=

2

5

=2.5m

So, the height of tower = 2.5m

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