Question

The angle of elevation of top of a tower from top and bottom of a 50m high building is observed to be 30°and 45°. Find height of tower

Answer 1

Given:

✭ Height of building = 50 m

✭ Angle of elevation from top of the building = 30°

✭ Angle of elevation from bottom of the building = 45°

To Find:

◈ Height of the tower

Solution:

Let

›› DC be the height of the building = 50 m

›› AE = x

Hence,

⪼ Height of the tower = AE + AB

⪼ Height of the tower = 50 + x m

Consider ΔABC,

➢ tan 45° = AB/BC

➢ tan 45° = x + 50/BC

➢ 1 = x + 50/BC

➢ BC = x + 50 -eq(1)

Consider ΔADE

➝ tan 30° = AE/DE

➝ tan 30° = x/DE

➝ 1/√3 = x/DE

➝ DE = √3 x -eq(2)

From equation 1 and 2, LHS are equal

Hence

➳ √3 x = x + 50

➳ √3x - x = 50

➳ x ( √3 - 1) = 50

➳ x = 50/√3 - 1

➳ x = 50 (√3 + 1)/2

➳ x = 25(√3 + 1)m

Hence,

Height of the tower = 50 + 25 (√3 + 1)

»» 50 + 68.3

»» 118.3 m

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Answer 2

Answer:

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Step-by-step explanation: