Question

The angle of elevation of an aeroplane as observed from a point 10cm above ground is found to be 30° & the angle of depression of the reflection in lake is found to be 60°. Determine the height of the aeroplane from the ground.

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Answer 1

A N S W E R :

• The height of the aeroplane is 20 cm.

Given :

• Angle of elevation of an aeroplane as observed from a point 10cm above the ground is 30°

• Angle of depression of the reflection in lake is 60°

• Height of the aeroplane from the ground

To find :

• Find Height of the aeroplane ?

Solution :

• Consider triangle ABF

=> tan∅ = Opposite/Adjacent

=> tan 30° = AB/BF

=> 1/√3 = (h - 10)/BF

=> BF = (h - 10)/√3 (equation 1)

• Consider triangle BFD

=> tan∅ = Opposite/Adjacent

=> tan 60° = BD/BF

=> √3 = h + 10/BF

=> BF = (h + 10)/√3 (equation 2)

From equation (1) and equation (2)

=> h - 10√3 = h + 10/√3

=> h - 10 = (h + 10)/3

=> 3h - 30 = h + 10

=> 2h = 40

=> h = 40cm