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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

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Attachment:

GRE If a can range from 45° to 60.jpg [ 11.56 KiB | Viewed 1075 times ]

If a can range from 45° to 60°, which of the following are possible values for y ?

Indicate all such values.

2

3

4

5

6

7

8

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Re: If a can range from 45° to 60°, which of the following are possible va
[#permalink]
08 Dec 2022, 18:56

explanation?

If a can range from 45° to 60°, which of the following are possible va
[#permalink]
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 1042 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 1017 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 1042 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 1017 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!

Re: If a can range from 45° to 60°, which of the following are possible va
[#permalink]
11 Dec 2022, 06:00

Expert Reply

OE

Given that the angle ranges from 45° to 60°, you need to plug in values for angle a and find a special triangle to solve for y. If a is 45°, the triangle’s sides are \(x, x, x \sqrt{2}\). It doesn’t matter what the hypotenuse is; x = 4, which means y also is 4. If a is 60°, the triangle’s sides are \(x, x \sqrt{3}, 2x\). The shortest side of the triangle would be the one on the x-axis. Since x = 4, then \(y = 4 \sqrt{3}\) or approximately 6.93. So the correct answers range from 4 to 6.93. Choices (C), (D), and (E) are all correct.

_________________

Given that the angle ranges from 45° to 60°, you need to plug in values for angle a and find a special triangle to solve for y. If a is 45°, the triangle’s sides are \(x, x, x \sqrt{2}\). It doesn’t matter what the hypotenuse is; x = 4, which means y also is 4. If a is 60°, the triangle’s sides are \(x, x \sqrt{3}, 2x\). The shortest side of the triangle would be the one on the x-axis. Since x = 4, then \(y = 4 \sqrt{3}\) or approximately 6.93. So the correct answers range from 4 to 6.93. Choices (C), (D), and (E) are all correct.

_________________

gmatclubot

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