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The angles of elevation of the top of a temple, from the foot and the top of a building 48 m high, are 60° and 30° respectively. The height of the temple is more than the building. The height of the temple is -
- a)75 m
- b)72 m
- c)60 m
- d)64 m
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The angles of elevation of the top of a temple, from the foot and the ...
The given data can be represented diagrammatically as follows where AD is the building and BC is the temple.
In ΔABC,
tan 60o = BC/AB
⇒ √3 = (BE + EC)/AB (∵ AD = BE = 48 m)
⇒ AB = (48 + EC)/√3 ….(1)
In ΔDEC,
tan 30o = EC/DE
⇒ 1/√3 = EC/AB (∵ DE = AB)
⇒ AB = √3EC ….(2)
Equating (1) and (2). We get,
(48 + EC)/√3 = √3EC
⇒ 3EC = 48 + EC
⇒ EC = 48/2 = 24 m
∴ The height of the temple = 48 + 24 = 72 m
Most Upvoted Answer
The angles of elevation of the top of a temple, from the foot and the ...
The given data can be represented diagrammatically as follows where AD is the building and BC is the temple.
In ΔABC,
tan 60o = BC/AB
⇒ √3 = (BE + EC)/AB (∵ AD = BE = 48 m)
⇒ AB = (48 + EC)/√3 ….(1)
In ΔDEC,
tan 30o = EC/DE
⇒ 1/√3 = EC/AB (∵ DE = AB)
⇒ AB = √3EC ….(2)
Equating (1) and (2). We get,
(48 + EC)/√3 = √3EC
⇒ 3EC = 48 + EC
⇒ EC = 48/2 = 24 m
∴ The height of the temple = 48 + 24 = 72 m
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Community Answer
The angles of elevation of the top of a temple, from the foot and the ...
The given data can be represented diagrammatically as follows where AD is the building and BC is the temple.
In ΔABC,
tan 60o = BC/AB
⇒ √3 = (BE + EC)/AB (∵ AD = BE = 48 m)
⇒ AB = (48 + EC)/√3 ….(1)
In ΔDEC,
tan 30o = EC/DE
⇒ 1/√3 = EC/AB (∵ DE = AB)
⇒ AB = √3EC ….(2)
Equating (1) and (2). We get,
(48 + EC)/√3 = √3EC
⇒ 3EC = 48 + EC
⇒ EC = 48/2 = 24 m
∴ The height of the temple = 48 + 24 = 72 m
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The angles of elevation of the top of a temple, from the foot and the top of a building 48 m high, are 60° and 30° respectively. The height of the temple is more than the building. The height of the temple is -a)75 mb)72 mc)60 md)64 mCorrect answer is option 'B'. Can you explain this answer?
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