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If the angle of elevation of the top of a tower from two points at the distance x and y meter from the base and in the same straight line with it are complementary, then the height of the tower is?
- a)√(x/y)
- b)√xy
- c)√(x+y)
- d)√(x-y)
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
If the angle of elevation of the top of a tower from two points at th...
Let AB be tower and C and D be the point of observation on AC. < />
AC = Xm, AD = Ym
S0,CD = x − ym
tanθ = h / x
And tan(90 - θ) = h/y
=> h / x x h / y = 1
=> h2 = xy
=> h = √xym
Most Upvoted Answer
If the angle of elevation of the top of a tower from two points at th...
Given:
- Angle of elevation of the top of a tower from two points at the distance x and y meters from the base and in the same straight line with it are complementary.
To Find:
- The height of the tower.
Approach:
To solve this problem, we can use trigonometry and the concept of complementary angles.
Let's assume that the height of the tower is 'h' meters.
From the given information, we can form the following right-angled triangles:
Triangle 1:
- Base: x meters
- Height: h meters
- Angle of elevation: θ1
Triangle 2:
- Base: y meters
- Height: h meters
- Angle of elevation: θ2
Since the angles of elevation are complementary, we have the following relationship:
θ1 + θ2 = 90°
Using trigonometry, we can relate the angles of elevation to the sides of the triangles:
Triangle 1:
tan(θ1) = h/x
Triangle 2:
tan(θ2) = h/y
Solution:
Using the relationship between the angles of elevation, we have:
θ1 + θ2 = 90°
Since tan(90°) = ∞, we can rewrite the equation as:
tan(θ1) + tan(θ2) = tan(90°)
Now, substituting the values of tan(θ1) and tan(θ2) from the triangles:
h/x + h/y = ∞
To simplify the equation, we can take the reciprocal of both sides:
1/(h/x + h/y) = 0
Simplifying further, we get:
xy/(x + y) = 0
Since the numerator cannot be zero, we can cancel out the denominator:
xy = 0
This implies that either x = 0 or y = 0, which is not possible as the distance cannot be zero.
Hence, the equation xy/(x + y) = 0 has no valid solution.
Therefore, the height of the tower cannot be determined using the given information.
- Angle of elevation of the top of a tower from two points at the distance x and y meters from the base and in the same straight line with it are complementary.
To Find:
- The height of the tower.
Approach:
To solve this problem, we can use trigonometry and the concept of complementary angles.
Let's assume that the height of the tower is 'h' meters.
From the given information, we can form the following right-angled triangles:
Triangle 1:
- Base: x meters
- Height: h meters
- Angle of elevation: θ1
Triangle 2:
- Base: y meters
- Height: h meters
- Angle of elevation: θ2
Since the angles of elevation are complementary, we have the following relationship:
θ1 + θ2 = 90°
Using trigonometry, we can relate the angles of elevation to the sides of the triangles:
Triangle 1:
tan(θ1) = h/x
Triangle 2:
tan(θ2) = h/y
Solution:
Using the relationship between the angles of elevation, we have:
θ1 + θ2 = 90°
Since tan(90°) = ∞, we can rewrite the equation as:
tan(θ1) + tan(θ2) = tan(90°)
Now, substituting the values of tan(θ1) and tan(θ2) from the triangles:
h/x + h/y = ∞
To simplify the equation, we can take the reciprocal of both sides:
1/(h/x + h/y) = 0
Simplifying further, we get:
xy/(x + y) = 0
Since the numerator cannot be zero, we can cancel out the denominator:
xy = 0
This implies that either x = 0 or y = 0, which is not possible as the distance cannot be zero.
Hence, the equation xy/(x + y) = 0 has no valid solution.
Therefore, the height of the tower cannot be determined using the given information.
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If the angle of elevation of the top of a tower from two points at the distance x and y meter from the base and in the same straight line with it are complementary, then the height of the tower is?a)√(x/y)b)√xyc)√(x+y)d)√(x-y)Correct answer is option 'B'. Can you explain this answer?
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If the angle of elevation of the top of a tower from two points at the distance x and y meter from the base and in the same straight line with it are complementary, then the height of the tower is?a)√(x/y)b)√xyc)√(x+y)d)√(x-y)Correct answer is option 'B'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about If the angle of elevation of the top of a tower from two points at the distance x and y meter from the base and in the same straight line with it are complementary, then the height of the tower is?a)√(x/y)b)√xyc)√(x+y)d)√(x-y)Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the angle of elevation of the top of a tower from two points at the distance x and y meter from the base and in the same straight line with it are complementary, then the height of the tower is?a)√(x/y)b)√xyc)√(x+y)d)√(x-y)Correct answer is option 'B'. Can you explain this answer?.
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