GMAT Exam > GMAT Questions > Two ships are sailing in the sea on the two s...
Start Learning for Free
Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30º and 45º respectively. If the lighthouse is 100 m high, the distance between the two ships is:
- a)300 m
- b)173 m
- c)273 m
- d)200 m
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Two ships are sailing in the sea on the two sides of a lighthouse. The...
Let BD be the lighthouse and A and C be the positions of the ships.
Then, BD = 100 m,
BAD = 30° , 
BCD = 45°
Distance between the two ships
= AC = BA + BC
=100√3+100=100(√3+1)=1003+100=100(3+1)
= 100(1.73+1) = 100 × 2.73 = 273 m
Most Upvoted Answer
Two ships are sailing in the sea on the two sides of a lighthouse. The...
Understanding the Problem
To find the distance between the two ships based on the angles of elevation to the top of the lighthouse, we can apply trigonometry. The lighthouse is 100 m tall, and the angles of elevation from the ships are 30° and 45°.
Identifying the Right Triangles
- Ship A (Angle of elevation: 30°)
- Ship B (Angle of elevation: 45°)
Using the properties of right triangles, we can set up two equations.
Calculating Distances
1. For Ship A (30° angle):
- Using the tangent function:
- tan(30°) = height / distance from Ship A
- tan(30°) = 100 / dA
- dA = 100 / tan(30°) = 100 / (1/√3) = 100√3 ≈ 173.21 m
2. For Ship B (45° angle):
- Using the tangent function:
- tan(45°) = height / distance from Ship B
- tan(45°) = 100 / dB
- dB = 100 / tan(45°) = 100 / 1 = 100 m
Finding the Total Distance Between the Ships
- The total distance between the two ships is:
- Total distance = dA + dB
- Total distance = 173.21 m + 100 m ≈ 273.21 m
Conclusion
Thus, the distance between the two ships is approximately 273 m, which corresponds to option 'C'.
To find the distance between the two ships based on the angles of elevation to the top of the lighthouse, we can apply trigonometry. The lighthouse is 100 m tall, and the angles of elevation from the ships are 30° and 45°.
Identifying the Right Triangles
- Ship A (Angle of elevation: 30°)
- Ship B (Angle of elevation: 45°)
Using the properties of right triangles, we can set up two equations.
Calculating Distances
1. For Ship A (30° angle):
- Using the tangent function:
- tan(30°) = height / distance from Ship A
- tan(30°) = 100 / dA
- dA = 100 / tan(30°) = 100 / (1/√3) = 100√3 ≈ 173.21 m
2. For Ship B (45° angle):
- Using the tangent function:
- tan(45°) = height / distance from Ship B
- tan(45°) = 100 / dB
- dB = 100 / tan(45°) = 100 / 1 = 100 m
Finding the Total Distance Between the Ships
- The total distance between the two ships is:
- Total distance = dA + dB
- Total distance = 173.21 m + 100 m ≈ 273.21 m
Conclusion
Thus, the distance between the two ships is approximately 273 m, which corresponds to option 'C'.
|
Explore Courses for GMAT exam
|
|
Similar GMAT Doubts
Top Courses for GMATView all
Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30º and 45º respectively. If the lighthouse is 100 m high, the distance between the two ships is:a)300 mb)173 mc)273 md)200 mCorrect answer is option 'C'. Can you explain this answer?
Question Description
Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30º and 45º respectively. If the lighthouse is 100 m high, the distance between the two ships is:a)300 mb)173 mc)273 md)200 mCorrect answer is option 'C'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30º and 45º respectively. If the lighthouse is 100 m high, the distance between the two ships is:a)300 mb)173 mc)273 md)200 mCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30º and 45º respectively. If the lighthouse is 100 m high, the distance between the two ships is:a)300 mb)173 mc)273 md)200 mCorrect answer is option 'C'. Can you explain this answer?.
Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30º and 45º respectively. If the lighthouse is 100 m high, the distance between the two ships is:a)300 mb)173 mc)273 md)200 mCorrect answer is option 'C'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30º and 45º respectively. If the lighthouse is 100 m high, the distance between the two ships is:a)300 mb)173 mc)273 md)200 mCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30º and 45º respectively. If the lighthouse is 100 m high, the distance between the two ships is:a)300 mb)173 mc)273 md)200 mCorrect answer is option 'C'. Can you explain this answer?.
Solutions for Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30º and 45º respectively. If the lighthouse is 100 m high, the distance between the two ships is:a)300 mb)173 mc)273 md)200 mCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
Download more important topics, notes, lectures and mock test series for GMAT Exam by signing up for free.
Here you can find the meaning of Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30º and 45º respectively. If the lighthouse is 100 m high, the distance between the two ships is:a)300 mb)173 mc)273 md)200 mCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30º and 45º respectively. If the lighthouse is 100 m high, the distance between the two ships is:a)300 mb)173 mc)273 md)200 mCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30º and 45º respectively. If the lighthouse is 100 m high, the distance between the two ships is:a)300 mb)173 mc)273 md)200 mCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30º and 45º respectively. If the lighthouse is 100 m high, the distance between the two ships is:a)300 mb)173 mc)273 md)200 mCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30º and 45º respectively. If the lighthouse is 100 m high, the distance between the two ships is:a)300 mb)173 mc)273 md)200 mCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice GMAT tests.
|
|
Explore Courses for GMAT exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup