Question

a statue 1.6 metre tall stands on the top of an pedestal for a point on the ground the angle of elevation of the top of a statue is 60 degree and from the same point of angle of elevation of the top of a pedestal is 45 degree find the height of a pedestal
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Answer 1

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Step-by-step explanation:

Answer 2

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• Let AB be the height of statue.

• D is the point on the ground from where the elevation is taken.

To Find: Height of pedestal = BC = AC – AB

From figure,

In right triangle BCD,

$\mapsto$tan 45° = BC/CD

$\mapsto$1 = BC/CD

$\mapsto$BC = CD ….(1)

Again,

In right ΔACD,

tan 60° =√3 = AB+BC/CD

$\mapsto$√3 CD = 1.6 + BC

$\mapsto$√3BC = 1.6 + BC (using equation (1)

$\mapsto$√3BC – BC = 1.6

$\mapsto$BC(√3-1) = 1.6

$\mapsto$BC = 1.6/(√3-1) m

BC=0.8(√3+1)

Thus, the height of the pedestal is 0.8(√3+1) m.