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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?
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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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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?
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