Question

When the sun's altitude increases form ${30}^o$ to ${60}^o$, the length of the shadow of a tower decreases by $100$ metres. Find the height of the tower.

• A. $70m$
• B. $55m$
• C. $86.6m$
• D. $93.5m$

Answer 1

The correct option is C $86.6m$

Let the length of the shadow from the foot of the tower be y when the altitude is ${60}^0$
Let the height of the tower be h.
Hence
$\tan {60}^0=\frac{h}{y}=\sqrt{3}$
Hence
$h=y\sqrt{3}$
Now
$\tan {30}^0=\frac{1}{\sqrt{3}}=\frac{h}{100+y}$
Hence
$100+y=h\sqrt{3}$
Hence
$100+y=3y$
or
$2y=100$
$y=50m$
Hence
$h=\sqrt{3}.50m$
$=86.6m$