GMAT Math : Calculating the length of the hypotenuse of an acute / obtuse triangle

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

22 Diagnostic Tests 693 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #591 : Gmat Quantitative Reasoning

The largest angle of an obtuse isosceles triangle has a measure of $120^{\circ}$ $\displaystyle 120^{\circ}$. If the length of the two equivalent sides is $\displaystyle 11$, what is the length of the hypotenuse?

Possible Answers:

$11\sqrt{3}$ $\displaystyle 11\sqrt{3}$

$22\sqrt{3}$ $\displaystyle 22\sqrt{3}$

$\frac{11}{2}\sqrt{3}$ $\displaystyle \frac{11}{2}\sqrt{3}$

$11\sqrt{6}$ $\displaystyle 11\sqrt{6}$

Correct answer:

$11\sqrt{3}$ $\displaystyle 11\sqrt{3}$

Explanation:

The height of the obtuse isosceles triangle bisects the $120^{\circ}$ $\displaystyle 120^{\circ}$ angle and forms two congruent right triangles. The hypotenuse of each of these triangles is either side of equivalent length, and we can see that the base of either triangle makes up half of the hypotenuse of the obtuse isosceles triangle. Because we know the angle opposite each base is half of $120^{\circ}$ $\displaystyle 120^{\circ}$, or $60^{\circ}$ $\displaystyle 60^{\circ}$, we can use the sine of this angle to find the length of the base. As there are two congruent right triangles that make up the obtuse isosceles triangle, the length of either base makes up half of the overall hypotenuse, so we then multiply the result by $\displaystyle 2$ to obtain the final answer. In the following solution, $\displaystyle b$ is the length of the base of one of the right triangles, $\displaystyle l$ is the length of the two equivalent sides, and $\displaystyle c$ is the length of the hypotenuse:

$\sin60^{\circ}=\frac{b}{l}$ $\displaystyle \sin60^{\circ}=\frac{b}{l}$

$\frac{\sqrt{3}}{2}=\frac{b}{11}\rightarrow b=\frac{11}{2}\sqrt{3}$ $\displaystyle \frac{\sqrt{3}}{2}=\frac{b}{11}\rightarrow b=\frac{11}{2}\sqrt{3}$

$c=2b=2\left(\frac{11}{2}\sqrt{3}\right)=11\sqrt{3}$ $\displaystyle c=2b=2\left(\frac{11}{2}\sqrt{3}\right)=11\sqrt{3}$

Report an Error

All GMAT Math Resources

22 Diagnostic Tests 693 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

LSAT Tutors in Phoenix, Reading Tutors in Atlanta, Algebra Tutors in Atlanta, Biology Tutors in Denver, Spanish Tutors in New York City, Math Tutors in Atlanta, SAT Tutors in San Francisco-Bay Area, GMAT Tutors in Dallas Fort Worth, Biology Tutors in Chicago, LSAT Tutors in Dallas Fort Worth

Popular Courses & Classes

Spanish Courses & Classes in Boston, SSAT Courses & Classes in Dallas Fort Worth, GMAT Courses & Classes in Washington DC, MCAT Courses & Classes in Denver, Spanish Courses & Classes in Denver, MCAT Courses & Classes in Los Angeles, GRE Courses & Classes in Seattle, GMAT Courses & Classes in Chicago, GMAT Courses & Classes in Phoenix, SAT Courses & Classes in Dallas Fort Worth

Popular Test Prep

SAT Test Prep in Denver, ISEE Test Prep in Washington DC, LSAT Test Prep in Houston, SAT Test Prep in Miami, SAT Test Prep in Chicago, GMAT Test Prep in Chicago, SSAT Test Prep in San Francisco-Bay Area, LSAT Test Prep in Dallas Fort Worth, GRE Test Prep in San Diego, GRE Test Prep in Chicago

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

Email address:
Your name:
Feedback:

GMAT Math : Calculating the length of the hypotenuse of an acute / obtuse triangle

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #591 : Gmat Quantitative Reasoning

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details