It is currently 23 Mar 2023, 02:50 |

Customized

for You

Track

Your Progress

Practice

Pays

- Mar
**23**### MBA Admission Goals: Identifying Your North Star that Gets You Admitted

10:00 AM PDT

-10:30 AM PDT

Your past experiences and achievable goals are key to getting admitted to a top-ranked business school. Join Sia Admission founder Susan Berishaj, on March 23, 2023, at 10 AM ET, where she will guide you to develop your goals for MBA admission success! - Mar
**23**### Draft a top school MBA application in a week

04:00 PM PDT

-05:00 PM PDT

In this video, Maria Wich-Vila, founder of ApplicantLab teaches how to draft a competitive MBA application quickly. In this session, she will cover: * Which actions to prioritize with the time you have left, and more. - Mar
**23**### MBA Journeys: Insights from IIMA PGPX Student Panel

09:00 PM IST

-10:00 PM IST

What does IIM Executive MBA or ISB PGP look for? Join GOALisB consultant and admits to know what it takes to get into a top MBA program in India and get your queries answered - Mar
**27**### Should you waive the GMAT/GRE?

04:00 PM EDT

-05:00 PM EDT

Wondering if you should waive the GMAT/GRE? In this quick tips video, Personal MBA Coach Founder, Scott Edinburgh, discusses when it may be a good idea to waive the GMAT/GRE - Mar
**28**### Decision Making Guide

04:00 PM PDT

-05:00 PM PDT

Wondering how to choose the right school and program type? Check out the Personal MBA Coach MBA Decision Making guide! - Mar
**29**### New hourly packages! The world has changed and so have we!

08:00 PM PDT

-09:00 PM PDT

Starting at $975 and offering up to $545 of savings, our new Amplify Hourly Packages offer structure and support in certain high-value areas (story development, resume, essays, interviewing) to help get your applications across the finish line.

If a can range from 45° to 60°, which of the following are possible va
[#permalink]
08 Dec 2022, 14:24

Expert Reply

Question Stats:

Attachment:

GRE If a can range from 45° to 60.jpg [ 11.56 KiB | Viewed 350 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

_________________

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 310 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 298 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 310 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 298 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

Moderators:

Multiple-choice Questions — Select One or More Answer Choices |
||

## Hi Guest,Here are updates for you: |