Question

 A statue 1.8 m tall stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top and bottom of the statue are 60 degree and 45 degree. Find the height of the pedestal​

Answer 1

Ans root 3 +1

hope it may help u

Answer 2

Given:

A statue 1.8 m tall stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top and bottom of the statue are 60 degrees and 45 degrees. Find the height of the pedestal​

To find:

The height of the pedestal​

Solution:

Let's say "x" meters represents the height of the pedestal.

From the figure, we get

"AB" = 1.8 m → height of the statue

"BC" = x m → height of the pedestal

"CD" → distance between the point and foot of the pedestal

"∠BDC" = 45° → angle of elevation of the bottom of the statue

"∠ADC" = 60° → angle of elevation of the top of the statue

We know,

$\boxed{tan\: \theta = \frac{Perpendicular}{Base}}$

In Δ BCD, we get

$tan\: 45\°= \frac{BC}{CD}}$

$\implies tan\: 45\°= \frac{x}{CD}}$

$\implies 1 = \frac{x}{CD}}$

$\implies CD = x$ . . . (1)

In Δ ACD, we get

$tan\: 60\°= \frac{AC}{CD}}$

on substituting from (1) and BC = x, we get

$\implies tan\: 60\°= \frac{1.8 + x}{x}}$

$\implies \sqrt{3} = \frac{1.8 + x}{x}}$

$\implies \sqrt{3}x = 1.8 + x$

$\implies x (\sqrt{3} - 1) = 1.8$

$\implies x =\frac{1.8}{\sqrt{3} - 1}$

$\implies x =\frac{1.8}{\sqrt{3} - 1} \times \frac{\sqrt{3} +1}{\sqrt{3} +1 }$

$\implies x =\frac{1.8(\sqrt{3} +1)}{(\sqrt{3})^2 - 1^2}$

$\implies x =\frac{1.8(\sqrt{3} +1)}{3 - 1}$

$\implies x =\frac{1.8(\sqrt{3} +1)}{2}$

$\implies \bold{x =0.9(\sqrt{3} +1)}$

or

$x =\frac{1.8}{\sqrt{3} - 1}$

Taking √3 = 1.732

$\implies x =\frac{1.8}{0.732}$

$\implies \bold{x = 2.45 \:m}$

Thus, the height of the pedestal is → 0.9(√3 + 1) m or 2.45 m.

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