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

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Answer 2

Answer:

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The height of the aeroplane is 20 cm

Explanation

Given

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

Angle of depression of the reflection in Lake is 60°

Height of the aeroplane from the ground

To Find

Height of the aeroplane

Solution

✭ Consider triangle ABF

→ tanθ = Opposite/Adjacent

→ tan 30° =AB/BF

→ 1/√3 = (h - 10)/BF

→ BF = (h - 10) √3 ❲ eq(1) ❳

✭ Consider triangle BFD

→ tanθ = Opposite/Adjacent

→ tan 60° = BD/BF

→ √3 = h + 10/BF

→ BF = (h + 10)/√3 ❲ eq(2) ❳

From eq(1) and eq(2)

→ h - 10√3 = h + 10/√3

→ h - 10 = (h + 10)/3

→ 3h - 30 = h + 10

→ 2h = 40

→ h = 20 cm