Question

A statue of 1.6 m tall stands on a top of pedestal from a point on the ground the angle of elevation of the top of statue is 60 and 45 degree from the same point of top of pedestal then find the height of pedestal.

Answer 1

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Answer 2

$\bold{height \: of \: pedestal = 0.8 \times ( \sqrt{3} + 1)}$

$\bold{step - by - step \: explaination}$

Let AB be the pedestal of height h meters and BC be the statue of height 1.6m.

Let D be any point on the ground such that,

$\angle{bda} = 45 \degree \: and \: \angle{cda} = 60 \degree$

Now,
$in \: \triangle{bda} \: we \: have$

$\: tan = 45 \degree = \frac{ab}{da} = \frac{h}{da}$

$1 = \frac{h}{da}$

$\therefore \: da = h...........(i)$

$again \: in \: \triangle{adc} \: we \: have$

$tan = 60 \degree = \frac{ac}{ad} = \frac{ab + bc}{ad}$

$\sqrt{3} = \frac{h + 1.6}{h} (from \: (i)$

$\sqrt{3} h = h + 1.6$

$( \sqrt{3} - 1)h = 1.6$

$\therefore \: h = \frac{1.6}{ \sqrt{3} - 1} = \frac{1.6}{ \sqrt{3} - 1} \times \frac{ \sqrt{3} + 1}{ \sqrt{3} + 1 }$

$= \frac{1.6( \sqrt{3} + 1)}{3 - 1} = \frac{1.6( \sqrt{3} + 1) }{2}$

$= 0.8 \times ( \sqrt{3} + 1)m$

That's it!!!!!