Question

A statue 1.6 metre 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 degree and from the same point the angle of elevation of the top of the pedestal is 45 degree find the height of the pedestal​ 1st CORRECT ANSWER WITH EXPLANATION BRAINLIEST

Answer 1

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Answer 2

Let the statue be AB of height 1.6m and Pedestal BC of height x meters...

From a Point D, which is on the ground, the angle of elevation for

pedestal is 45° and 60° for top of the statue.

In ΔBCD,

Tan45° = $\frac{Opposite}{adjacent}$ =$\frac{BC}{DC}$

=> $1=\frac{x}{DC}$

=>$DC = x$

Now, In ΔACD,

Tan60° =  $\frac{Opposite}{adjacent}$ = $\frac{1.6+x}{x}$

=> $\sqrt{3}x = 1.6 + x$

$x (\sqrt{3} - 1) = 1.6\\x = \frac{1.6}{sqrt{3} - 1} * \frac{\sqrt{3} + 1}{\sqrt{3} + 1} \\x = \frac{1.6(\sqrt{3} + 1)}{4}\\x = {0.4(\sqrt{3} + 1)$

Hope it helps

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