# 8. A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and from the same point the angle of elevation of the top of the pedestal is 45°. Find the height of the pedestal.

M manish

Let the height of the pedestal be $h$ m. and the height of the statue is 1.6 m.
the angle of elevation of the top of the statue and top of the pedestal is($\angle DCB=$ $60^o$ )and($\angle ACB=$ $45^o$) respectively.

Now,
In triangle $\Delta ABC$,
$\tan 45^o =1 =\frac{AB}{BC}=\frac{h}{BC}$
therefore,  BC = $h$ m

In triangle $\Delta CBD$,
$\\\Rightarrow \tan 60^o = \frac{BD}{BC}=\frac{h+1.6}{h}\\\\\Rightarrow \sqrt{3}= 1+\frac{1.6}{h}$
the value of  $h$ is $0.8(\sqrt{3}+1)$ m
Hence the height of the pedestal is  $0.8(\sqrt{3}+1)$m

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