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As observed from the top of a 100 m high lighthouse from the sea-level, the angles of depression of two ships are 30� and 45�. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships. [Use √3 = 1.732]?
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As observed from the top of a 100 m high lighthouse from the sea-level...
Understanding the Problem
To find the distance between two ships observed from a 100 m high lighthouse, we need to analyze the angles of depression given as 30° and 45°.
Setting Up the Diagram
- Imagine the lighthouse is point A (100 m high).
- Ship 1 is at point B, and Ship 2 is at point C.
- The angles of depression from the top of the lighthouse to the ships are 30° for Ship 1 and 45° for Ship 2.
Applying Trigonometry
- The angle of depression equals the angle of elevation from the ships to the lighthouse, leading us to use tangent function in right triangles.
Calculating Distances
- For Ship 1 (Angle of depression = 30°):
- Height of lighthouse = 100 m
- tan(30°) = opposite/adjacent = 100/distance to Ship 1 (d1)
- d1 = 100/tan(30°) = 100/(1/√3) = 100√3 ≈ 100 * 1.732 = 173.2 m
- For Ship 2 (Angle of depression = 45°):
- tan(45°) = opposite/adjacent = 100/distance to Ship 2 (d2)
- d2 = 100/tan(45°) = 100/1 = 100 m
Finding the Distance Between the Ships
- Distance between Ship 1 and Ship 2:
- Distance = d1 - d2 = 173.2 m - 100 m = 73.2 m
Final Result
The distance between the two ships is approximately 73.2 meters.
To find the distance between two ships observed from a 100 m high lighthouse, we need to analyze the angles of depression given as 30° and 45°.
Setting Up the Diagram
- Imagine the lighthouse is point A (100 m high).
- Ship 1 is at point B, and Ship 2 is at point C.
- The angles of depression from the top of the lighthouse to the ships are 30° for Ship 1 and 45° for Ship 2.
Applying Trigonometry
- The angle of depression equals the angle of elevation from the ships to the lighthouse, leading us to use tangent function in right triangles.
Calculating Distances
- For Ship 1 (Angle of depression = 30°):
- Height of lighthouse = 100 m
- tan(30°) = opposite/adjacent = 100/distance to Ship 1 (d1)
- d1 = 100/tan(30°) = 100/(1/√3) = 100√3 ≈ 100 * 1.732 = 173.2 m
- For Ship 2 (Angle of depression = 45°):
- tan(45°) = opposite/adjacent = 100/distance to Ship 2 (d2)
- d2 = 100/tan(45°) = 100/1 = 100 m
Finding the Distance Between the Ships
- Distance between Ship 1 and Ship 2:
- Distance = d1 - d2 = 173.2 m - 100 m = 73.2 m
Final Result
The distance between the two ships is approximately 73.2 meters.
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As observed from the top of a 100 m high lighthouse from the sea-level, the angles of depression of two ships are 30� and 45�. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships. [Use √3 = 1.732]?
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As observed from the top of a 100 m high lighthouse from the sea-level, the angles of depression of two ships are 30� and 45�. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships. [Use √3 = 1.732]? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about As observed from the top of a 100 m high lighthouse from the sea-level, the angles of depression of two ships are 30� and 45�. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships. [Use √3 = 1.732]? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for As observed from the top of a 100 m high lighthouse from the sea-level, the angles of depression of two ships are 30� and 45�. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships. [Use √3 = 1.732]?.
As observed from the top of a 100 m high lighthouse from the sea-level, the angles of depression of two ships are 30� and 45�. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships. [Use √3 = 1.732]? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about As observed from the top of a 100 m high lighthouse from the sea-level, the angles of depression of two ships are 30� and 45�. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships. [Use √3 = 1.732]? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for As observed from the top of a 100 m high lighthouse from the sea-level, the angles of depression of two ships are 30� and 45�. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships. [Use √3 = 1.732]?.
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As observed from the top of a 100 m high lighthouse from the sea-level, the angles of depression of two ships are 30� and 45�. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships. [Use √3 = 1.732]?, a detailed solution for As observed from the top of a 100 m high lighthouse from the sea-level, the angles of depression of two ships are 30� and 45�. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships. [Use √3 = 1.732]? has been provided alongside types of As observed from the top of a 100 m high lighthouse from the sea-level, the angles of depression of two ships are 30� and 45�. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships. [Use √3 = 1.732]? theory, EduRev gives you an
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