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If from the top of a lighthouse 100 metre high the angle of depression of a boat is tan-1(5/12) then the distance (in metre) between the boat and the lighthouse is equal to:
- a)125/3
- b)120
- c)240
- d)260
Correct answer is option 'A'. Can you explain this answer?
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If from the top of a lighthouse 100 metre high the angle of depressio...
Given that the height of lighthouse = 100m
View all questions of this test
and the angle of depression of the boat is tan-1 5/12
X = 240
∴ The distance between the boat and the lighthouse is 240 m.
Most Upvoted Answer
If from the top of a lighthouse 100 metre high the angle of depressio...
Given information:
- The height of the lighthouse is 100 meters.
- The angle of depression of the boat from the top of the lighthouse is tan-1(5/12).
To find the distance between the boat and the lighthouse, we can use trigonometry.
Let's consider the height of the lighthouse as the opposite side of the angle of depression, and the distance between the boat and the lighthouse as the adjacent side.
Using the tangent function, we have:
tan(angle of depression) = opposite/adjacent
tan(tan-1(5/12)) = 100/adjacent
Since the tangent of an angle is equal to the ratio of the opposite side to the adjacent side, tan(tan-1(5/12)) simplifies to:
5/12 = 100/adjacent
To solve for the adjacent side (distance between the boat and the lighthouse), we can cross-multiply:
5 * adjacent = 12 * 100
adjacent = (12 * 100) / 5
adjacent = 1200 / 5
adjacent = 240 meters
Therefore, the distance between the boat and the lighthouse is 240 meters.
Hence, the correct answer is option 'A' (240/3).
- The height of the lighthouse is 100 meters.
- The angle of depression of the boat from the top of the lighthouse is tan-1(5/12).
To find the distance between the boat and the lighthouse, we can use trigonometry.
Let's consider the height of the lighthouse as the opposite side of the angle of depression, and the distance between the boat and the lighthouse as the adjacent side.
Using the tangent function, we have:
tan(angle of depression) = opposite/adjacent
tan(tan-1(5/12)) = 100/adjacent
Since the tangent of an angle is equal to the ratio of the opposite side to the adjacent side, tan(tan-1(5/12)) simplifies to:
5/12 = 100/adjacent
To solve for the adjacent side (distance between the boat and the lighthouse), we can cross-multiply:
5 * adjacent = 12 * 100
adjacent = (12 * 100) / 5
adjacent = 1200 / 5
adjacent = 240 meters
Therefore, the distance between the boat and the lighthouse is 240 meters.
Hence, the correct answer is option 'A' (240/3).
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If from the top of a lighthouse 100 metre high the angle of depression of a boat is tan-1(5/12) then the distance (in metre) between the boat and the lighthouse is equal to:a)125/3b)120c)240d)260Correct answer is option 'A'. Can you explain this answer?
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If from the top of a lighthouse 100 metre high the angle of depression of a boat is tan-1(5/12) then the distance (in metre) between the boat and the lighthouse is equal to:a)125/3b)120c)240d)260Correct answer is option 'A'. 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 from the top of a lighthouse 100 metre high the angle of depression of a boat is tan-1(5/12) then the distance (in metre) between the boat and the lighthouse is equal to:a)125/3b)120c)240d)260Correct answer is option 'A'. 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 from the top of a lighthouse 100 metre high the angle of depression of a boat is tan-1(5/12) then the distance (in metre) between the boat and the lighthouse is equal to:a)125/3b)120c)240d)260Correct answer is option 'A'. Can you explain this answer?.
If from the top of a lighthouse 100 metre high the angle of depression of a boat is tan-1(5/12) then the distance (in metre) between the boat and the lighthouse is equal to:a)125/3b)120c)240d)260Correct answer is option 'A'. 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 from the top of a lighthouse 100 metre high the angle of depression of a boat is tan-1(5/12) then the distance (in metre) between the boat and the lighthouse is equal to:a)125/3b)120c)240d)260Correct answer is option 'A'. 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 from the top of a lighthouse 100 metre high the angle of depression of a boat is tan-1(5/12) then the distance (in metre) between the boat and the lighthouse is equal to:a)125/3b)120c)240d)260Correct answer is option 'A'. Can you explain this answer?.
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