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28 Jul 2021, 04:15
Kudos
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
57% (02:29) correct
43%
(02:55)
wrong
based on 60
sessions
History
Date
Time
Result
Not Attempted Yet
A boat, stationed at the North of a 300-feet high lighthouse, is making an angle of 30° with the top of the lighthouse. Simultaneously, another boat, stationed at the East of the same lighthouse, is making an angle of 45° with the top of the lighthouse. What will be the shortest distance between these two boats? Assume both the boats are of negligible dimensions.
A 300 feet
B 400 feet
C 500 feet
D 600 feet
E 700 feet
A 300 feet
B 400 feet
C 500 feet
D 600 feet
E 700 feet
28 Jul 2021, 19:53
Kudos
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Bunuel
This question involves three dimensions (not at the same time), and the north and east directions are not useful until the last step.
First, let us take the sea level view. From the first sentence, we can draw a 30-60-90 triangle with the shorter leg being 300 feet. Then we can figure out the distance of the boat, it is \(300*\sqrt{3} = 300\sqrt{3}\) feet.
Next, we use the lighthouse height to calculate how far the east boat is away from the lighthouse. The east boat makes a 45-45-90 triangle so the distance is simply \(300\) feet as well.
Finally, let us go to the bird's eye view. The lighthouses are \(300\sqrt{3}\) feet and 300 feet away, and they make a right angle. Using the Pythagorean theorem they have a distance of \(\sqrt{300^2*3 + 300^2} = 300*\sqrt{3 + 1} = 600\) feet.
Ans: D
28 Jul 2021, 23:06
Kudos
Bookmarks
Quote:
Step 1: Understanding the question
Using the relation of special right angle triangle 30° : 60° : 90° as x : x√3 : 2x
The boat stationed at the North of a 300-feet high lighthouse, making an angle of 30° with the top of the lighthouse, is 300√3 feet away from the lighthouse (opposite to 60°).
Using the relation of special right angle triangle 45° : 45° : 90° as x : x : x√2
The boat stationed at the East of the same lighthouse, is making an angle of 45° with the top of the lighthouse, is 300 feet away from the lighthouse (opposite to 45°).
Step 2: Calculation
The two boats are making right angle with each other, hence using Pythagorean theorem to find distance between them.
Distance between the two boats = √[\((300√3)^2 + (300)^2\)] = 300 * √[\((√3)^2 + 1^2\)] = 300*2 = 600 feet
D is correct
