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

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

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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