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The angles of elevation of the top of a tower from two points on the ground at distances 8m and 18m from the base of the tower and in the same straight line with it are complementary. The height of the tower is
- a)8m
- b)16m
- c)12m
- d)18m
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The angles of elevation of the top of a tower from two points on the g...
- Distances of two points from the base of the tower are 8 m
- The angles of elevation are complementary, meaning their sum is 90 degree
- Let the height of the tower be h.
From the first point:
From the second point:
For complementary angles:
Substituting values from equations (1) and (2):
Most Upvoted Answer
The angles of elevation of the top of a tower from two points on the g...
Let AB= height of the tower=?,
and angle of elevations be ,
angle ACB =@ and angle ADB=90-@( as both the angles are complementary angles),
in right triangle ABC tan@=AB/BC,
tan@=AB/8---(1).,
in right triangle ABD tan(90-@)=AB/18,
we know that tan (90-@)=cot@,
so, cot@=AB/18,--(2),
Cot@=1/tan@,
from( 1)&(2),
AB/8=1/AB/18,
AB/8=18/AB,
AB²=18×8,
AB=√18×8=√3×3×2×2×2×2=3×2×2=12m
and angle of elevations be ,
angle ACB =@ and angle ADB=90-@( as both the angles are complementary angles),
in right triangle ABC tan@=AB/BC,
tan@=AB/8---(1).,
in right triangle ABD tan(90-@)=AB/18,
we know that tan (90-@)=cot@,
so, cot@=AB/18,--(2),
Cot@=1/tan@,
from( 1)&(2),
AB/8=1/AB/18,
AB/8=18/AB,
AB²=18×8,
AB=√18×8=√3×3×2×2×2×2=3×2×2=12m
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Community Answer
The angles of elevation of the top of a tower from two points on the g...
Explanation:
Let the height of the tower be 'h' meters.
Let the angles of elevation from the two points be 'θ' and '90° - θ', respectively.
We know that tan θ = height/distance
So, tan θ = h/8 ... (1)
And, tan (90° - θ) = height/distance
So, tan (90° - θ) = h/18 ... (2)
We also know that tan (90° - θ) = cot θ
So, (2) can be written as cot θ = h/18 ... (3)
Now, using (1) and (3), we can write:
h/8 × h/18 = 1
=> h² = 8 × 18
=> h² = 144
=> h = √144
=> h = 12 meters
Therefore, the height of the tower is 12 meters. Answer: (c)
Let the height of the tower be 'h' meters.
Let the angles of elevation from the two points be 'θ' and '90° - θ', respectively.
We know that tan θ = height/distance
So, tan θ = h/8 ... (1)
And, tan (90° - θ) = height/distance
So, tan (90° - θ) = h/18 ... (2)
We also know that tan (90° - θ) = cot θ
So, (2) can be written as cot θ = h/18 ... (3)
Now, using (1) and (3), we can write:
h/8 × h/18 = 1
=> h² = 8 × 18
=> h² = 144
=> h = √144
=> h = 12 meters
Therefore, the height of the tower is 12 meters. Answer: (c)
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The angles of elevation of the top of a tower from two points on the ground at distances 8m and 18m from the base of the tower and in the same straight line with it are complementary. The height of the tower isa)8mb)16mc)12md)18mCorrect answer is option 'C'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The angles of elevation of the top of a tower from two points on the ground at distances 8m and 18m from the base of the tower and in the same straight line with it are complementary. The height of the tower isa)8mb)16mc)12md)18mCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The angles of elevation of the top of a tower from two points on the ground at distances 8m and 18m from the base of the tower and in the same straight line with it are complementary. The height of the tower isa)8mb)16mc)12md)18mCorrect answer is option 'C'. Can you explain this answer?.
The angles of elevation of the top of a tower from two points on the ground at distances 8m and 18m from the base of the tower and in the same straight line with it are complementary. The height of the tower isa)8mb)16mc)12md)18mCorrect answer is option 'C'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The angles of elevation of the top of a tower from two points on the ground at distances 8m and 18m from the base of the tower and in the same straight line with it are complementary. The height of the tower isa)8mb)16mc)12md)18mCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The angles of elevation of the top of a tower from two points on the ground at distances 8m and 18m from the base of the tower and in the same straight line with it are complementary. The height of the tower isa)8mb)16mc)12md)18mCorrect answer is option 'C'. Can you explain this answer?.
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