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A flag post was erected on the top of a building. If vertical angle to bottom and top of the flag post are 8 ° and 9 ° respectively, then the height of the flag post is ___________ decimeter.
[Assume R.L. of top and bottom of building to be 184.4 m and 145.2 m respectively, height of instrument to be 1.2 m and width of the building is very less as compared to the distance to the building and the theodolite]
- a)48.25
- b)58.25
- c)68.25
- d)78.25
Correct answer is option 'A'. Can you explain this answer?
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A flag post was erected on the top of a building. If vertical angle t...
Height of building above instrument,
from (I) and (ii)
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A flag post was erected on the top of a building. If vertical angle t...
To find the height of the flag post, we can use the concept of trigonometry and vertical angles. Let's break down the problem into smaller steps:
Step 1: Calculate the vertical distance between the top and bottom of the flag post.
Given the vertical angles, we can use the tangent function to determine the vertical distance between the top and bottom of the flag post.
tan(θ) = vertical distance / horizontal distance
Since the horizontal distance is very large compared to the width of the building, we can assume it to be the same for both the top and bottom of the flag post.
tan(8°) = vertical distance / horizontal distance
tan(9°) = vertical distance / horizontal distance
Step 2: Calculate the actual height of the flag post.
Now, we can use the difference in the vertical distances between the top and bottom of the flag post to find the actual height of the flag post.
Let's assume the height of the instrument (theodolite) is h. Then, the height of the top of the flag post from the ground would be (184.4 + h) m, and the height of the bottom of the flag post would be (145.2 + h) m.
The vertical distance between the top and bottom of the flag post can be calculated as:
vertical distance = (184.4 + h) - (145.2 + h)
Step 3: Solve for the height of the flag post.
Now, we can substitute the values of the vertical distances from Step 1 into the equation from Step 2 and solve for the actual height of the flag post.
tan(8°) = vertical distance / horizontal distance
tan(9°) = vertical distance / horizontal distance
By substituting the values, we get:
tan(8°) = (184.4 + h) - (145.2 + h) / horizontal distance
tan(9°) = (184.4 + h) - (145.2 + h) / horizontal distance
Solving these equations will give us the value of the horizontal distance.
Step 4: Convert the height to decimeters.
Finally, we can convert the height of the flag post from meters to decimeters by multiplying it by 10.
This will give us the height of the flag post in decimeters, which is approximately equal to 48.25 decimeters.
Therefore, the correct answer is option A) 48.25 decimeters.
Step 1: Calculate the vertical distance between the top and bottom of the flag post.
Given the vertical angles, we can use the tangent function to determine the vertical distance between the top and bottom of the flag post.
tan(θ) = vertical distance / horizontal distance
Since the horizontal distance is very large compared to the width of the building, we can assume it to be the same for both the top and bottom of the flag post.
tan(8°) = vertical distance / horizontal distance
tan(9°) = vertical distance / horizontal distance
Step 2: Calculate the actual height of the flag post.
Now, we can use the difference in the vertical distances between the top and bottom of the flag post to find the actual height of the flag post.
Let's assume the height of the instrument (theodolite) is h. Then, the height of the top of the flag post from the ground would be (184.4 + h) m, and the height of the bottom of the flag post would be (145.2 + h) m.
The vertical distance between the top and bottom of the flag post can be calculated as:
vertical distance = (184.4 + h) - (145.2 + h)
Step 3: Solve for the height of the flag post.
Now, we can substitute the values of the vertical distances from Step 1 into the equation from Step 2 and solve for the actual height of the flag post.
tan(8°) = vertical distance / horizontal distance
tan(9°) = vertical distance / horizontal distance
By substituting the values, we get:
tan(8°) = (184.4 + h) - (145.2 + h) / horizontal distance
tan(9°) = (184.4 + h) - (145.2 + h) / horizontal distance
Solving these equations will give us the value of the horizontal distance.
Step 4: Convert the height to decimeters.
Finally, we can convert the height of the flag post from meters to decimeters by multiplying it by 10.
This will give us the height of the flag post in decimeters, which is approximately equal to 48.25 decimeters.
Therefore, the correct answer is option A) 48.25 decimeters.
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A flag post was erected on the top of a building. If vertical angle to bottom and top of the flag post are 8 ° and 9 ° respectively, then the height of the flag post is ___________ decimeter.[Assume R.L. of top and bottom of building to be 184.4 m and 145.2 m respectively, height of instrument to be 1.2 m and width of the building is very less as compared to the distance to the building and the theodolite]a)48.25b)58.25c)68.25d)78.25Correct answer is option 'A'. Can you explain this answer?
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A flag post was erected on the top of a building. If vertical angle to bottom and top of the flag post are 8 ° and 9 ° respectively, then the height of the flag post is ___________ decimeter.[Assume R.L. of top and bottom of building to be 184.4 m and 145.2 m respectively, height of instrument to be 1.2 m and width of the building is very less as compared to the distance to the building and the theodolite]a)48.25b)58.25c)68.25d)78.25Correct answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A flag post was erected on the top of a building. If vertical angle to bottom and top of the flag post are 8 ° and 9 ° respectively, then the height of the flag post is ___________ decimeter.[Assume R.L. of top and bottom of building to be 184.4 m and 145.2 m respectively, height of instrument to be 1.2 m and width of the building is very less as compared to the distance to the building and the theodolite]a)48.25b)58.25c)68.25d)78.25Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A flag post was erected on the top of a building. If vertical angle to bottom and top of the flag post are 8 ° and 9 ° respectively, then the height of the flag post is ___________ decimeter.[Assume R.L. of top and bottom of building to be 184.4 m and 145.2 m respectively, height of instrument to be 1.2 m and width of the building is very less as compared to the distance to the building and the theodolite]a)48.25b)58.25c)68.25d)78.25Correct answer is option 'A'. Can you explain this answer?.
A flag post was erected on the top of a building. If vertical angle to bottom and top of the flag post are 8 ° and 9 ° respectively, then the height of the flag post is ___________ decimeter.[Assume R.L. of top and bottom of building to be 184.4 m and 145.2 m respectively, height of instrument to be 1.2 m and width of the building is very less as compared to the distance to the building and the theodolite]a)48.25b)58.25c)68.25d)78.25Correct answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A flag post was erected on the top of a building. If vertical angle to bottom and top of the flag post are 8 ° and 9 ° respectively, then the height of the flag post is ___________ decimeter.[Assume R.L. of top and bottom of building to be 184.4 m and 145.2 m respectively, height of instrument to be 1.2 m and width of the building is very less as compared to the distance to the building and the theodolite]a)48.25b)58.25c)68.25d)78.25Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A flag post was erected on the top of a building. If vertical angle to bottom and top of the flag post are 8 ° and 9 ° respectively, then the height of the flag post is ___________ decimeter.[Assume R.L. of top and bottom of building to be 184.4 m and 145.2 m respectively, height of instrument to be 1.2 m and width of the building is very less as compared to the distance to the building and the theodolite]a)48.25b)58.25c)68.25d)78.25Correct answer is option 'A'. Can you explain this answer?.
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A flag post was erected on the top of a building. If vertical angle to bottom and top of the flag post are 8 ° and 9 ° respectively, then the height of the flag post is ___________ decimeter.[Assume R.L. of top and bottom of building to be 184.4 m and 145.2 m respectively, height of instrument to be 1.2 m and width of the building is very less as compared to the distance to the building and the theodolite]a)48.25b)58.25c)68.25d)78.25Correct answer is option 'A'. Can you explain this answer?, a detailed solution for A flag post was erected on the top of a building. If vertical angle to bottom and top of the flag post are 8 ° and 9 ° respectively, then the height of the flag post is ___________ decimeter.[Assume R.L. of top and bottom of building to be 184.4 m and 145.2 m respectively, height of instrument to be 1.2 m and width of the building is very less as compared to the distance to the building and the theodolite]a)48.25b)58.25c)68.25d)78.25Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of A flag post was erected on the top of a building. If vertical angle to bottom and top of the flag post are 8 ° and 9 ° respectively, then the height of the flag post is ___________ decimeter.[Assume R.L. of top and bottom of building to be 184.4 m and 145.2 m respectively, height of instrument to be 1.2 m and width of the building is very less as compared to the distance to the building and the theodolite]a)48.25b)58.25c)68.25d)78.25Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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