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There are two buildings, one on each bank of a river, just opposite to each other. One building is 36 m high. From the top of the this building, the angles of depression of the top and foot of the other building are 30° and 45° respectively. Find the height of the other building?
- a)15.3 m
- b)10.3 m
- c)60.3 m
- d)30.3 m
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
There are two buildings, one on each bank of a river, just opposite to...
As per the given data,
Let AB and CD be the two buildings, and AC be the river with a length of x meters
Let AB and CD be the two buildings, and AC be the river with a length of x meters
Let us consider AB be the building of height = 36 m and CD be the height of other building of h meters
⇒ ∠ACB = 45° and ∠EDB = 30°
From ΔABC, we get
⇒ AB/AC = tan 45°
⇒ 1 = AB/AC
⇒ AB = AC = 36 m
∴ DE = AC = 36 m
From ΔEDB, we get
⇒ tan 30° = BE/DE
⇒ 1/√3 = BE/DE
⇒ BE = DE/√3 = 36/√3 = 20.7 m
We know that CD = AE = AB – BE = (36 - 20.7) m = 15.3 m
∴ height of the other building = 15.3 m
Most Upvoted Answer
There are two buildings, one on each bank of a river, just opposite to...
Given information:
- Height of one building: 36 m
- Angle of depression from the top of one building to the top of the other building: 30°
- Angle of depression from the top of one building to the foot of the other building: 45°
Calculating the height of the other building:
- Let the height of the other building be 'h' meters.
- We can consider the distance between the two buildings as 'x' meters.
Using trigonometry:
- tan 30° = (h - 36) / x [Angle of depression of 30°]
- tan 45° = h / x [Angle of depression of 45°]
Solving the equations:
- tan 30° = (h - 36) / x
=> 1/√3 = (h - 36) / x
=> x = √3(h - 36) [Equation 1]
- tan 45° = h / x
=> 1 = h / x
=> x = h [Equation 2]
Equating Equation 1 and Equation 2:
√3(h - 36) = h
=> √3h - 36√3 = h
=> √3h - h = 36√3
=> h(√3 - 1) = 36√3
=> h = 36√3 / (√3 - 1)
=> h ≈ 15.3 m
Therefore, the height of the other building is approximately 15.3 meters. Hence, the correct answer is option A.
- Height of one building: 36 m
- Angle of depression from the top of one building to the top of the other building: 30°
- Angle of depression from the top of one building to the foot of the other building: 45°
Calculating the height of the other building:
- Let the height of the other building be 'h' meters.
- We can consider the distance between the two buildings as 'x' meters.
Using trigonometry:
- tan 30° = (h - 36) / x [Angle of depression of 30°]
- tan 45° = h / x [Angle of depression of 45°]
Solving the equations:
- tan 30° = (h - 36) / x
=> 1/√3 = (h - 36) / x
=> x = √3(h - 36) [Equation 1]
- tan 45° = h / x
=> 1 = h / x
=> x = h [Equation 2]
Equating Equation 1 and Equation 2:
√3(h - 36) = h
=> √3h - 36√3 = h
=> √3h - h = 36√3
=> h(√3 - 1) = 36√3
=> h = 36√3 / (√3 - 1)
=> h ≈ 15.3 m
Therefore, the height of the other building is approximately 15.3 meters. Hence, the correct answer is option A.
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There are two buildings, one on each bank of a river, just opposite to each other. One building is 36 m high. From the top of the this building, the angles of depression of the top and foot of the other building are 30° and 45° respectively. Find the height of the other building?a)15.3 mb)10.3 mc)60.3 md)30.3 mCorrect answer is option 'A'. Can you explain this answer?
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There are two buildings, one on each bank of a river, just opposite to each other. One building is 36 m high. From the top of the this building, the angles of depression of the top and foot of the other building are 30° and 45° respectively. Find the height of the other building?a)15.3 mb)10.3 mc)60.3 md)30.3 mCorrect answer is option 'A'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about There are two buildings, one on each bank of a river, just opposite to each other. One building is 36 m high. From the top of the this building, the angles of depression of the top and foot of the other building are 30° and 45° respectively. Find the height of the other building?a)15.3 mb)10.3 mc)60.3 md)30.3 mCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are two buildings, one on each bank of a river, just opposite to each other. One building is 36 m high. From the top of the this building, the angles of depression of the top and foot of the other building are 30° and 45° respectively. Find the height of the other building?a)15.3 mb)10.3 mc)60.3 md)30.3 mCorrect answer is option 'A'. Can you explain this answer?.
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