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,

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 agoA balloon is connected to a meteorological ground station by a cable of length 215 m inclined at 60° to the horizontal. Determine the height of the balloon from the ground. Assume that there is no slack in the cable.

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