Question

From a point on the ground $40m$ away from the foot of tower, the angle of elevation of the top of the tower is ${30}^o$. The angle of elevation to the top of a water tank (on the top of the tower) is ${45}^o$. Find
the depth of the tank.

• A. $8.71m$
• B. $10m$
• C. $16.91m$
• D. $13m$

Answer 1

The correct option is C $16.91m$

Let the height of the tower be $h.$
Let the height of the tank be $x.$
Hence total length of the structure $=h+x.$

Now applying trigonometric ratios, we get
$\tan {45}^0=\frac{h+x}{40m}$
$=1$

Hence
$h+x=40m$ ...(i)

Also
$\tan {30}^0=\frac{h}{40}=\frac{1}{\sqrt{3}}$

Hence
$h=\frac{40\sqrt{3}}{3}$
$=23.09m$

Now
$x=40-\frac{40}{\sqrt{3}}$

$=40\left(\frac{\sqrt{3}-1}{\sqrt{3}}\right)$

$=16.905m$