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As observed from the top of the hundred metre height lighthouse from the sea level the angles of the depression of two ships are 30 degree and 45 degree if one if exactly behind the other on the same side of the lighthouse find the distance between take root 3 is equals to 1.732?
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As observed from the top of the hundred metre height lighthouse from t...
Given data:
- Height of lighthouse = 100 metres
- Angle of depression of first ship = 30 degrees
- Angle of depression of second ship = 45 degrees
- Distance between the two ships = x metres
Calculating the distance between the two ships:
To find the distance between the two ships, we can consider the right-angled triangles formed by the lighthouse, the first ship, and the second ship.
Calculating the distance to the first ship:
- Let h be the distance between the lighthouse and the first ship.
- tan(30 degrees) = 100/h
- h = 100/tan(30 degrees) = 100/(√3/3) = 100*3/√3 = 300/√3 = 100√3
Calculating the distance to the second ship:
- Let d be the distance between the lighthouse and the second ship.
- tan(45 degrees) = 100/d
- d = 100/tan(45 degrees) = 100/1 = 100
Calculating the distance between the two ships:
- Since the second ship is directly behind the first ship, the distance between the two ships is equal to the difference in their distances from the lighthouse.
- x = d - h = 100 - 100√3 = 100(1 - √3) = 100(1 - 1.732) = 100*-0.732 = -73.2
Therefore, the distance between the two ships is -73.2 metres.
- Height of lighthouse = 100 metres
- Angle of depression of first ship = 30 degrees
- Angle of depression of second ship = 45 degrees
- Distance between the two ships = x metres
Calculating the distance between the two ships:
To find the distance between the two ships, we can consider the right-angled triangles formed by the lighthouse, the first ship, and the second ship.
Calculating the distance to the first ship:
- Let h be the distance between the lighthouse and the first ship.
- tan(30 degrees) = 100/h
- h = 100/tan(30 degrees) = 100/(√3/3) = 100*3/√3 = 300/√3 = 100√3
Calculating the distance to the second ship:
- Let d be the distance between the lighthouse and the second ship.
- tan(45 degrees) = 100/d
- d = 100/tan(45 degrees) = 100/1 = 100
Calculating the distance between the two ships:
- Since the second ship is directly behind the first ship, the distance between the two ships is equal to the difference in their distances from the lighthouse.
- x = d - h = 100 - 100√3 = 100(1 - √3) = 100(1 - 1.732) = 100*-0.732 = -73.2
Therefore, the distance between the two ships is -73.2 metres.
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As observed from the top of the hundred metre height lighthouse from the sea level the angles of the depression of two ships are 30 degree and 45 degree if one if exactly behind the other on the same side of the lighthouse find the distance between take root 3 is equals to 1.732?
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As observed from the top of the hundred metre height lighthouse from the sea level the angles of the depression of two ships are 30 degree and 45 degree if one if exactly behind the other on the same side of the lighthouse find the distance between take root 3 is equals to 1.732? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about As observed from the top of the hundred metre height lighthouse from the sea level the angles of the depression of two ships are 30 degree and 45 degree if one if exactly behind the other on the same side of the lighthouse find the distance between take root 3 is equals to 1.732? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for As observed from the top of the hundred metre height lighthouse from the sea level the angles of the depression of two ships are 30 degree and 45 degree if one if exactly behind the other on the same side of the lighthouse find the distance between take root 3 is equals to 1.732?.
As observed from the top of the hundred metre height lighthouse from the sea level the angles of the depression of two ships are 30 degree and 45 degree if one if exactly behind the other on the same side of the lighthouse find the distance between take root 3 is equals to 1.732? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about As observed from the top of the hundred metre height lighthouse from the sea level the angles of the depression of two ships are 30 degree and 45 degree if one if exactly behind the other on the same side of the lighthouse find the distance between take root 3 is equals to 1.732? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for As observed from the top of the hundred metre height lighthouse from the sea level the angles of the depression of two ships are 30 degree and 45 degree if one if exactly behind the other on the same side of the lighthouse find the distance between take root 3 is equals to 1.732?.
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