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:-

• Ex 9.1 Q2 - A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30° with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree.

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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