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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
- e)220 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)
= 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...
Degrees and 45 degrees, respectively. If the distance between the two ships is 100 meters, what is the height of the lighthouse?
Let's assume that the height of the lighthouse is h meters.
From the first ship, the angle of elevation of the top of the lighthouse is 30 degrees. Therefore, we can use the tangent function to find the height of the lighthouse.
tan(30) = h / x
where x is the distance between the first ship and the lighthouse.
From the second ship, the angle of elevation of the top of the lighthouse is 45 degrees. Therefore, we can use the tangent function to find the height of the lighthouse.
tan(45) = h / (100 - x)
where (100 - x) is the distance between the second ship and the lighthouse.
Rearranging the first equation, we get:
h = x * tan(30)
Substituting this into the second equation, we get:
tan(45) = (x * tan(30)) / (100 - x)
Using the values of tan(30) = 1/sqrt(3) and tan(45) = 1, we can simplify the equation:
1 = (x * 1/sqrt(3)) / (100 - x)
Multiplying both sides by (100 - x) and sqrt(3), we get:
100 - x = x * sqrt(3)
Simplifying further, we get:
100 = x * (sqrt(3) + 1)
Dividing both sides by (sqrt(3) + 1), we get:
x = 100 / (sqrt(3) + 1)
Using a calculator, we can find the value of x ≈ 38.3 meters.
Substituting this value of x into the equation for h, we get:
h = 38.3 * tan(30)
Using the value of tan(30) = 1/sqrt(3), we can calculate the height of the lighthouse:
h ≈ 38.3 * (1/sqrt(3)) ≈ 22.2 meters
Therefore, the height of the lighthouse is approximately 22.2 meters.
Let's assume that the height of the lighthouse is h meters.
From the first ship, the angle of elevation of the top of the lighthouse is 30 degrees. Therefore, we can use the tangent function to find the height of the lighthouse.
tan(30) = h / x
where x is the distance between the first ship and the lighthouse.
From the second ship, the angle of elevation of the top of the lighthouse is 45 degrees. Therefore, we can use the tangent function to find the height of the lighthouse.
tan(45) = h / (100 - x)
where (100 - x) is the distance between the second ship and the lighthouse.
Rearranging the first equation, we get:
h = x * tan(30)
Substituting this into the second equation, we get:
tan(45) = (x * tan(30)) / (100 - x)
Using the values of tan(30) = 1/sqrt(3) and tan(45) = 1, we can simplify the equation:
1 = (x * 1/sqrt(3)) / (100 - x)
Multiplying both sides by (100 - x) and sqrt(3), we get:
100 - x = x * sqrt(3)
Simplifying further, we get:
100 = x * (sqrt(3) + 1)
Dividing both sides by (sqrt(3) + 1), we get:
x = 100 / (sqrt(3) + 1)
Using a calculator, we can find the value of x ≈ 38.3 meters.
Substituting this value of x into the equation for h, we get:
h = 38.3 * tan(30)
Using the value of tan(30) = 1/sqrt(3), we can calculate the height of the lighthouse:
h ≈ 38.3 * (1/sqrt(3)) ≈ 22.2 meters
Therefore, the height of the lighthouse is approximately 22.2 meters.
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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 me)220 mCorrect answer is option 'C'. Can you explain this answer?
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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 me)220 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 me)220 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 me)220 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 me)220 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 me)220 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 me)220 mCorrect answer is option 'C'. Can you explain this answer?.
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