Question

The shadow of a flagstaff is three times as long as the shadow of the flagstaff when the sun rays meet the ground at angle of ${60}^o$. Find the angle between the sun rays and ground at the time of the longer shadow.

• A. $\theta ={30}^o$
• B. $\theta ={60}^o$
• C. $\theta ={45}^o$
• D. $\theta ={15}^o$

Answer 1

The correct option is A $\theta ={30}^o$

Let the length of the shadow be $x$ when it makes an angle of ${60}^0$ at point C at the ground and $3x$ at an angle of $\theta$ at point D.

Let height of flagstaff be $h$

In right angled $\Delta ABC$.

$tan{60}^0=\frac{h}{x}$

$\to h=xtan{60}^0$ ..............(1)

In $\Delta BDA$

$tan\theta =\frac{h}{3x}$

$\to h=3xtan\theta$ ...............(2)

From (1) & (2) we get,

$xtan{60}^0=3xtan\theta$

$\to tan\theta =\frac{tan60}{3}$

$\to tan\theta =\frac{\sqrt{3}}{3}$

$\to tan\theta =\frac{\sqrt{3}\times \sqrt{3}}{3\times \sqrt{3}}$

$\to tan\theta =\frac{1}{\sqrt{3}}$

$\to \theta ={30}^0$