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A statue 1.46 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 $45 °$ . What will be the height of the pedestal using $3 =$ 1.73?

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0.73 3 + 2

0.73 3 + 1

0.72 3 + 1

0.83 3 + 1

answer is B.

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Detailed Solution

Given,
Statue height =1.46 m
Angle of elevation of the statue =

60 °

Angle of elevation of the top of the pedestal=

45 °

3 = 1.73

We draw diagram,
Question Image

We use the trigonometric identity,

tan θ = p e r p e n d i c u l a r b a s e

We get the value of AB from

Δ A B D

tan 45 ° = D B A B ⇒ 1 = h A B ∵ tan 45 ° = 1 ⇒ A B = h ....... (i)

We get value of AB from

Δ A B C

tan 60 ° = B D + D C A B ⇒ 3 = h + 1.46 A B ∵ tan 60 ° = 3 ⇒ A B = h + 1.46 3 ........ (i i)

We compare the equations (i) and (ii),

⇒ h = h + 1.46 3 ⇒ 3 h = h + 1.46 ⇒ 3 h − h = 1.46 ⇒ h 3 − 1 = 1.46

On rationalizing we get,

⇒ h = 1.46 3 − 1 × 3 + 1 3 + 1 ⇒ h = 1.46 3 + 1 (3) 2 + 3 × 1 − 3 × 1 + 1 × − 1 ⇒ h = 1.46 3 + 1 3 − 1 ⇒ h = 1.46 3 + 1 2 ⇒ h = 0.73 3 + 1

Thus, the height of Pedestal will be

0.73 3 + 1

m.
Therefore the correct option is 2.

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