Ex 9.1 Q8 - A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground

Ex 9.1 Q8 - 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.

Solution:-

Let,

*AB be the statue.

*BC be the pedestal.

*D be the point on ground from where

angle of elevation is measured.

To find: Height of pedestal i.e BC.

Given,

*Height of statue = AB = 1.6 m

*Angle of elevation of the top of

statue = ∠ADC = 60°

*Angle of elevation of the top of

pedestal = ∠BDC = 45°

*Since, the pedestal is perpendicular to the ground,

∴ ∠ACD = 90°

➙ In ∆BDC, ∠BCD = 90°

∴ tanD =

Opposite side of ∠D / Adjacent side of ∠D

∴ tan45° =

BC / CD

∴ 1 =

BC / CD

{ ∵ tan45° = 1 }

∴ CD = BC ------- (1)

➙ In ∆ADC, ∠ACD = 90°

∴ tanD =

Opposite side of ∠D / Adjacent side of ∠D

∴ tan60° =

AC / CD

∴ tan60° =

AC / BC

{ From (1) }

∴ tan60° =

AB + BC / BC

{ ∵ AC = AB + BC }

∴ tan60° =

1.6 + BC / BC

{ Given, AB = 1.6 }

∴ √3 =

1.6 + BC / BC

{ ∵ tan60° = √3 }

∴ √3BC = 1.6 + BC

∴ √3BC - BC = 1.6

∴ BC(√3 - 1) = 1.6

∴ BC =

1.6 / √3 - 1

*Multiplying Numerator and Denominator by √3 + 1,

∴ BC =

1.6 / √3 - 1

√3 + 1 / √3 + 1

*Using formula, (a + b) (a - b) = a² - b²

1.6(√3 + 1) / (√3)² - (1)²

1.6(√3 + 1) / 3 - 1

1.6(√3 + 1) / 2

= 0.8(√3 + 1)

∴ BC = 0.8(√3 + 1)

Hence,

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

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Try This..

✒ The angle of elevation of a cloud from a point 120 m above a lake is 30°, and the angle of depression of its reflection in the lake is 60°. Find the height of the cloud.

✒ A tower 10 m high casts a shadow 10 m long. Find the angle of elevation of the Sun.

✒ A ladder is leaning against a wall making an angle of 60° with the ground. If the foot is 2.5 m away from the wall, find the length of the ladder.

❌ Common Mistakes

Wrong triangle selection:
▸ Always match angles with the correct triangle (statue+pedestal vs pedestal alone).

Not rationalizing denominators:
▸ Especially when dealing with square roots like √3.

Forgetting units:
▸ Final answer should always include meters.

Mixing up ‘from’ and ‘to’ in angle of elevation:
▸ Visualizing the diagram helps eliminate this confusion.

📝 Related Questions:-

Queries Solved:-

Class 10 Ex 9.1

Ex 9.1 Q8 Class 10

Class 10 Ex 9.1 Q8

Class 10 Chap 9 Ex 9.1 Q8

Class 10 Some Applications Of Trigonometry

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Ex 9.1 Q8 - A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground

Ex 9.1 Q8 - 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.

Try This..

❌ Common Mistakes

📝 Related Questions:-

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