Question

A statue 1.46m 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 60m and from the same point the angle of elevation of the top of the pedestal is 45.Find the height of the pedestal

Answer 1

hope it's clear......

Answer 2

Answer:

$\red { Height \:of \: the \: Pedestal }\green {=1.994\:m }$

Step-by-step explanation:

Height of the Pedestal = AB = h m,

Height of the statue = BC = 1.46 m,

Then , AC = AB + BC = ( h + 1.46 ) m,

Distance between Pedestal and observation point = AD ,

$\angle ADB = 45\degree, \:\angle ADC = 60\degree$

$In \: \triangle ABD ,\\tan 45\degree = \frac{AB}{AD} = \frac{h}{x}$

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

$\implies x = h\:---(1)$

$In \: \triangle ADC ,\\tan 60\degree = \frac{AC}{AD}$

$\sqrt{3} = \frac{( h + 1.46 )}{x}$

$\implies x = \frac{(h+1.46)}{\sqrt{3}}\:---(2)$

$\implies h = \frac{(h+1.46)}{\sqrt{3}}\: [From \:(1) \:and \:(2)$

$\implies \sqrt{3}h = h + 1.46$

$\implies \sqrt{3}h - h = 1.46$

$\implies ( \sqrt{3} - 1) = 1.46$

$\implies ( 1.732 - 1)h = 1.46$

$\implies 0.732h = 1.46$

$\implies h = \frac{1.46}{0.732}$

$\implies h = 1.994\:m$

Therefore.,

$\red { Height \:of \: the \: Pedestal }\green {=1.994\:m }$

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