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  • 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.

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.

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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 = 2.9m
Hence the height of the pedestal is  2.9m

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