a man observes the angle of elevation of the top of the building to be 30°. he walks towards it in a horizontal line through its base. on covering 60m the angle of elevation changes to 60°. Find the height of the building
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EXPLANATION.
The angle of elevation of the top of the
building = 30°.
The angle of elevation changes to = 60°.
In right angled triangle <ACB.
Tan ø = P/B = Perpendicular/Base.
Tan 60° = AB/BC
→ √3 = AB / x
→ H = √3x ..........(1).
In right angled triangle <ADB.
Tan ø = P/B = Perpendicular/Base
Tan 30° = AB/BD
→ 1/√3 = H / DC + CB.
→ 1/√3 = √3x / 60 + x.
→ 3x = 60 + x.
→ 2x = 60.
→ x = 30 M.
→ AB = 30√3 M.
Heights of the building = 30√3 M.
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