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The figure represents the design of a drawbridge that spans a channel
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20 Jan 2015, 07:00
20 Jan 2015, 07:00
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Difficulty:
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Question Stats:
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41%
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The figure represents the design of a drawbridge that spans a channel 54 meters in width. If the two raisable sections are equal in length and overlap each other by a measure of 2 meters, what will be the clearance width of the bridge in meters, when the sections are raised to an angle of 60 degree ?
A) 25
B) 26
C) 27
D) 28
E) 54
Attachment:
1.png [ 9.08 KiB | Viewed 8977 times ]
Kudos for a correct solution.
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Re: The figure represents the design of a drawbridge that spans a channel
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22 Jan 2015, 19:09
22 Jan 2015, 19:09
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Answer = B = 26
Total span = 54 with overlap of 2 meters
Let "x" be the length of each non-overlap section
Then, x + 2 + x = 54
x = 26
Length of each arm = 26+2 = 28
Refer diagram below:
1.png [ 10.52 KiB | Viewed 7658 times ]
When this 28 meters arm is raised 60 degrees, it forms a 30 - 60 - 90 degree right triangle with 28 as its hypotenuse
Sides of 30:60:90 are in ratio \(1: \sqrt{3}:2\), so the side opposite to 30degree would be 14 (which is the non-cleared section of bridge)
Total clearance = 54 - 2*14 = 26
Total span = 54 with overlap of 2 meters
Let "x" be the length of each non-overlap section
Then, x + 2 + x = 54
x = 26
Length of each arm = 26+2 = 28
Refer diagram below:
Attachment:
1.png [ 10.52 KiB | Viewed 7658 times ]
When this 28 meters arm is raised 60 degrees, it forms a 30 - 60 - 90 degree right triangle with 28 as its hypotenuse
Sides of 30:60:90 are in ratio \(1: \sqrt{3}:2\), so the side opposite to 30degree would be 14 (which is the non-cleared section of bridge)
Total clearance = 54 - 2*14 = 26
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Re: The figure represents the design of a drawbridge that spans a channel
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19 Aug 2020, 07:11
19 Aug 2020, 07:11
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Bunuel
The figure represents the design of a drawbridge that spans a channel 54 meters in width. If the two raisable sections are equal in length and overlap each other by a measure of 2 meters, what will be the clearance width of the bridge in meters, when the sections are raised to an angle of 60 degree ?
A) 25
B) 26
C) 27
D) 28
E) 54
Attachment:
1.png
Kudos for a correct solution.
The two raisable sections are equal in length and overlap each other by a measure of 2 meters
The bridge spans a distance of 54 meters.
So, if both sections were 27 meters long, there would be no overlap.
Since the sections overlap by 2 meters, we know that each section is 28 meters long.
So, our diagram looks like this:
If we draw vertical lines from the tips of each section, you see that we have special 30-60-90 triangles hiding in our diagram.
In the each of the right triangles, the hypotenuse has length 28
So, the lengths of the sides opposite the 30 degree angles must be 14.
To find the value of x, we can write the following equation: 14 + x + 14 = 54
Simplify: x + 28 = 54
Subtract 28 from both sides of the equation to get: x = 26
Answer: B
Cheers,
Brent
)
