GMAT Math : DSQ: Calculating the length of the side of a right triangle

Study concepts, example questions & explanations for GMAT Math

Create An Account

All GMAT Math Resources

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

Example Questions

Example Question #21 : Dsq: Calculating The Length Of The Side Of A Right Triangle

$\bigtriangleup ABC$ is a right triangle with right angle $\angle B$ . Evaluate .

Statement 1: AC = 22 and $m \angle A = 30^{\circ }$ .

Statement 2: BC = 11 and $m \angle C = 60^{\circ }$ .

Possible Answers:

BOTH statements TOGETHER are insufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Correct answer:

EITHER statement ALONE is sufficient to answer the question.

Explanation:

Either statement alone is sufficient.

From either statement alone, it can be determined that $m \angle A = 30^{\circ }$ and $m \angle C = 60^{\circ }$ ; each statement gives one angle measure, and the other can be calculated by subtracting the first from $90^{\circ }$ , since the acute angles of a right triangle are complementary.

Also, since $\angle B$ is the right angle, $\overline{AC}$ is the hypotenuse, and $\overline{BC}$ , opposite the $30 ^{\circ }$ angle, the shorter leg of a 30-60-90 triangle. From either statement alone, the 30-60-90 Theorem can be used to find the length of longer leg $\overline{AB}$ . From Statement 1 alone, $\overline{AB}$ has length $\frac{\sqrt{3}}{2}$ times that of the hypotenuse, or $\frac{\sqrt{3}}{2} \cdot 22 = 11\sqrt{3}$ . From Statement 2 alone, $\overline{AB}$ has length $\sqrt{3}$ of the shorter leg, or $11\sqrt{3}$ .

Report an Error

Example Question #141 : Triangles

The longest side of a right triangle has a length of $13\textup{ in}$ . If the base of the triangle is $5\textup{ in}$ long, how long is the other side of the triangle?

Possible Answers:

$12\textup{in}$

$9\textup{in}$

$11\textup{in}$

$8\textup{in}$

$10\textup{in}$

Correct answer:

$12\textup{in}$

Explanation:

This is a Pythagorean theorem question. The lengths of a right triangle are related by the following equation: $a^{2}+b^{2}=c^{2}.$ In the problem statement, $c=13\textup{in}$ and $a=5\textup{in.}$ Therefore, $b^{2}= c^{2}-a^{2}= 13^{2}-5^{2}=169-25=144. b=\sqrt{144}=12\textup{in.}$

Report an Error

All GMAT Math Resources

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

Popular Subjects

Computer Science Tutors in San Diego, English Tutors in San Francisco-Bay Area, French Tutors in Seattle, SSAT Tutors in Atlanta, Math Tutors in Seattle, ISEE Tutors in Los Angeles, Math Tutors in Washington DC, LSAT Tutors in Denver, Calculus Tutors in Boston, Chemistry Tutors in Denver

Popular Courses & Classes

GRE Courses & Classes in Chicago, ISEE Courses & Classes in Denver, GMAT Courses & Classes in Denver, GRE Courses & Classes in Miami, MCAT Courses & Classes in Philadelphia, SAT Courses & Classes in San Francisco-Bay Area, Spanish Courses & Classes in Chicago, GRE Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in Dallas Fort Worth, ACT Courses & Classes in Phoenix

Popular Test Prep

SAT Test Prep in San Diego, GRE Test Prep in Dallas Fort Worth, SAT Test Prep in Philadelphia, ACT Test Prep in San Diego, ISEE Test Prep in Denver, ACT Test Prep in Houston, LSAT Test Prep in San Francisco-Bay Area, SSAT Test Prep in Miami, ISEE Test Prep in Houston, ISEE Test Prep in San Diego

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 : DSQ: Calculating the length of the side of a right triangle

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #21 : Dsq: Calculating The Length Of The Side Of A Right Triangle

Example Question #141 : Triangles

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details