Question

A vertical tower stands on a horizontal plane and is surmounted by a vertical flag staff of height 5 meters. At a point on the plane, the angles of elevation of the bottom and the top of the flag staff are respectively 30° and 60°. Find the height of the tower.

• A.
  2.5 m
• B.
  5 m
• C.
  3.2 m
• D.
  3 m

Answer 1

The correct option is A

2.5 m
Let height of tower be ‘h’ m (i.e. BC)
Let the distance of the point from the base of the tower be ‘x’ m.
In right angle triangle BCD, we have

$tan{30}^{\circ }=\frac{BC}{DC}$

$\frac{1}{\surd 3}=\frac{h}{x}$

$x=h\surd 3\dots ..\left(i\right)$

Now, in ΔACD,
$tan{60}^{\circ }=\frac{AC}{DC}$

$\surd 3=\frac{(5+h)}{x}$

$\surd 3x=5+h$

$\surd 3\left(h\surd 3\right)=5+h\left[using\right(i\left)\right]$

$3h=5+h$

$2h=5$

$h=\frac{5}{2}=2.5m$

Hence, the height of tower is 2.5 m.