Question
Download Solution PDFA woman is standing 30 m away from her house. An angle of elevation from the top of her is 30° towards the top of house and angle of elevation from her foot is 60° towards the top of the house. Find the total height of the house and woman.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
A woman is standing 30 m away from her house. An angle of elevation from the top of her is 30° towards the top of house and angle of elevation from her foot is 60° towards the top of the house
Calculation:
In ΔABC,
⇒ tan30° = AB/BC
⇒ 1/√3 = AB/30
⇒ AB = 30/√3
⇒ AB = 30√3/(√3 × √3)
⇒ AB = 10√3 m
In ΔAED,
⇒ tan60° = AE/ED
⇒ √3 = (AB + BE)/30
⇒ AB + BE = 30√3
⇒ BE = 30√3 – 10√3
⇒ BE = 20√3 m
Total height of the house = 10√3 + 20√3 = 30√3
Height of the women = CD = BE = 20√3
Total height of the house and women = 30√3 + 20√3 = 50√3
∴ Total height of the house and women is 50√3
Last updated on Jun 27, 2025
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