Question

A statue, $1.6m$ tall, stands on the top of pedestal. From a point on the ground, the angle of elevation of the top of the statue is ${60}^o$ and from the same point the angle of elevation of the top of the pedestal is ${45}^o$. Find height of the pedestal.

• A. Height of the pedestal$=0.2(\sqrt{7}-1)$ m
  
• B. Height of the pedestal$=0.8(\sqrt{3}+1)$ m
• C. Height of the pedestal$=1.6(\sqrt{5}+1)$ m
• D. Height of the pedestal$=1.9(\sqrt{11}-1)$ m

Answer 1

Answer: (B)

Height of the pedestal$=0.8(\sqrt{3}+1)$ m

Now from the figure
$\angle FBC={45}^0$
$\angle ABC={60}^0$
Therefore
$\tan {45}^0=\frac{h}{m}=1$
Hence $h=m$
And
$\tan {60}^0$
$=\frac{1.6+h}{h}$
$=\sqrt{3}$
Hence
$1.6+h=\sqrt{3}h$
$1.6=h(\sqrt{3}-1)$
$h=\frac{1.6}{\sqrt{3}-1}$
$=\frac{1.6(\sqrt{3}+1)}{2}$
$=0.8(\sqrt{3}+1)$
$=2.185m$
Hence the height of the pedestal is $2.185m$.