c) A tower has a flag pole on it, and the tower has a height of 40 m. The angle of elevationof the top of the tower and the flag pole are respectively 30° and 45° to an observerstanding on the horizontal line from the foot of the tower. Find the length of the flagpole correct to two significant figures.[4]
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On a horizontal plane, there is a vertical tower with a flagpole on the top of the tower. At a point 9 meters away from the foot of the tower the angle of elevation of the top and bottom of the flagpole are 60
o
and 30
o
respectively. Find the height of the tower and the flagpole mounted on it.
In the figure flag pole is AB, BC is tower and CD is base.
In △ACD,
⇒ tan60
o
=
DC
AC
⇒
60
=
9
AC
∴ AC=9
3
m
In △DBC,
⇒ tan30
o
=
DC
BC
⇒
3
1
=
9
BC
∴ BC=
3
9
=3
3
m
⇒ AC=AB+BC
⇒ AB=AC−BC
⇒ AB=9
3
−3
3
=6
3
m
∴ Height of the flag pole is 6
3
m and that of tower is 3
3
m.
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