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If a can range from 45° to 60°, which of the following are possible va
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08 Dec 2022, 14:24
08 Dec 2022, 14:24
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54% (01:39) correct
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GRE If a can range from 45° to 60.jpg [ 11.56 KiB | Viewed 1551 times ]
If a can range from 45° to 60°, which of the following are possible values for y ?
Indicate all such values.
2
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Re: If a can range from 45° to 60°, which of the following are possible va
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08 Dec 2022, 18:56
08 Dec 2022, 18:56
explanation?
If a can range from 45° to 60°, which of the following are possible va
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10 Dec 2022, 12:27
10 Dec 2022, 12:27
Since angle a has a minimum of 45 degrees and a maximum of 60 degrees, then the y coordinate will a range of values between the minimum and maximum angles.
Let's fine the minimum first:
45 degrees.jpg [ 17.88 KiB | Viewed 1522 times ]
If angle a = 45 degrees, then we have special 45-45-90 isosceles triangle with sides 4-4-4 sq root 2. That means in this case y = 4
Now for the maximum:
60 degrees.jpg [ 18.73 KiB | Viewed 1479 times ]
If angle a = 60 degrees, then we have another special triangle, a 30-60-90 triangle. This has the unique properties of having a side length ratio of (small leg) : (larger leg) : (hypotenuse) = x : x square root 3: 2x.
That means y = 4 square root 3 which is approximately equal to 6.9
So now that we have the minimum and maximum values for y, we can set up an inequality:
4 ≤ y ≤ 6.9 -----> Answer Choices C , D and E
Hope this helps!
Let's fine the minimum first:
Attachment:
45 degrees.jpg [ 17.88 KiB | Viewed 1522 times ]
If angle a = 45 degrees, then we have special 45-45-90 isosceles triangle with sides 4-4-4 sq root 2. That means in this case y = 4
Now for the maximum:
Attachment:
60 degrees.jpg [ 18.73 KiB | Viewed 1479 times ]
If angle a = 60 degrees, then we have another special triangle, a 30-60-90 triangle. This has the unique properties of having a side length ratio of (small leg) : (larger leg) : (hypotenuse) = x : x square root 3: 2x.
That means y = 4 square root 3 which is approximately equal to 6.9
So now that we have the minimum and maximum values for y, we can set up an inequality:
4 ≤ y ≤ 6.9 -----> Answer Choices C , D and E
Hope this helps!
