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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
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The angles of elevation of the top of a temple, from the foot and the ...
Understanding the Problem
To find the height of the temple based on the angles of elevation from a building, we need to set up the scenario using trigonometric principles. The height of the building is given as 48 m, and we have two angles of elevation to consider: 60° from the foot of the building and 30° from the top.
Step 1: Define Variables
- Let the height of the temple be H meters.
- The distance from the building to the temple’s base will be denoted as d meters.
Step 2: Using Trigonometry
- From the Foot of the Building (60° Angle):
- Using the tangent function:
tan(60°) = H / d
=> H = d * √3
- From the Top of the Building (30° Angle):
- The height from the top of the building to the temple's top is (H - 48) m:
tan(30°) = (H - 48) / d
=> H - 48 = d / √3
Step 3: Solve the Equations
Now we have two equations:
1. H = d * √3
2. H - 48 = d / √3
Substituting equation 1 into equation 2:
d * √3 - 48 = d / √3
Multiplying through by √3 to eliminate the fraction:
3d - 48√3 = d
This simplifies to:
2d = 48√3
=> d = 24√3
Now substitute d back into equation 1:
H = 24√3 * √3 = 72 m
Conclusion
Thus, the height of the temple is 72 m (option b).
To find the height of the temple based on the angles of elevation from a building, we need to set up the scenario using trigonometric principles. The height of the building is given as 48 m, and we have two angles of elevation to consider: 60° from the foot of the building and 30° from the top.
Step 1: Define Variables
- Let the height of the temple be H meters.
- The distance from the building to the temple’s base will be denoted as d meters.
Step 2: Using Trigonometry
- From the Foot of the Building (60° Angle):
- Using the tangent function:
tan(60°) = H / d
=> H = d * √3
- From the Top of the Building (30° Angle):
- The height from the top of the building to the temple's top is (H - 48) m:
tan(30°) = (H - 48) / d
=> H - 48 = d / √3
Step 3: Solve the Equations
Now we have two equations:
1. H = d * √3
2. H - 48 = d / √3
Substituting equation 1 into equation 2:
d * √3 - 48 = d / √3
Multiplying through by √3 to eliminate the fraction:
3d - 48√3 = d
This simplifies to:
2d = 48√3
=> d = 24√3
Now substitute d back into equation 1:
H = 24√3 * √3 = 72 m
Conclusion
Thus, the height of the temple is 72 m (option b).
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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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