Question

A vertical tower stands on the plane ground and is surmounted by a flag-staff of height 7 m. If the angle of elevation of the bottom of the flag-staff from a point on the ground is 30º and that of the top of the flag-staff is 60º, then the height of the tower is

• A. 2.5 m
• B. 3.5 m
• C. 4.5 m
• D. 7 m

Answer 1

The correct option is B 3.5 m

Let AB be the flag-staff and BC be the tower.
Let BC = x.
$In\Delta BCD,$
$\tan {30}^{\circ }=\frac{BC}{CD}$
$\Rightarrow \frac{1}{\sqrt{3}}=\frac{x}{CD}$
$\Rightarrow CD=\sqrt{3}x$ ...(i)
Now, $in\Delta ACD,$
$\tan {60}^{\circ }=\frac{AC}{DC}$
$\Rightarrow \sqrt{3}=\frac{7+x}{\sqrt{3}x}$ $[\because AC=AB+BC,\text{from (i)}]$
$\Rightarrow 3x=7+x$
$\Rightarrow 2x=7$
$\Rightarrow x=\frac{7}{2}=3.5m$
So, the height of the tower is 3.5 m.
Hence, the correct answer is option (b).