A statue, 1.6 m 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° and from the same point the angle of elevation of the top of the pedestal is 45°. Find the height of the pedestal.

Asked by Abhisek | 1 year ago |  81

1 Answer

Solution :-

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

C:\Users\User\Desktop\NCERT\images\trig8.jpg

From figure,

In right triangle BCD,

tan 45° = \( \dfrac{BC}{CD}\)

1 = \( \dfrac{BC}{CD}\)

BC = CD …..(1)

Again,

In right ΔACD,

tan 60° = \( \dfrac{AC}{AD}\)

\( \sqrt{3}\) = \( \dfrac{AB+BC}{CD}\)

\( \sqrt{3}CD\) = 1.6 + BC

\( \sqrt{3}BC\) = 1.6 + BC (using equation (1)

\( \sqrt{3}BC\) – BC = 1.6

BC\( (\sqrt{3}-1)\) = 1.6

BC =\( \dfrac{(1.6)(\sqrt{3}+1)}{(\sqrt{3}-1)(\sqrt{3}+1)}\)

BC = \( 1.6\dfrac{(\sqrt{3}+1)}{2m}\)

BC = 0.8 \(( \sqrt{3}+1)\)

Thus, the height of the pedestal is 0.8\( ( \sqrt{3}+1)m\) .

Answered by Pragya Singh | 1 year ago

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