We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Create an account to track your scores
and create your own practice tests:

Create an Account Create a Practice Test

All HiSET: Math Resources

125 Practice Tests Question of the Day Flashcards Learn by Concept

Want to review HiSET: Math but don’t feel like sitting for a whole test at the moment? Varsity Tutors has you covered with thousands of different HiSET: Math flashcards! Our HiSET: Math flashcards allow you to practice with as few or as many questions as you like. Get some studying in now with our numerous HiSET: Math flashcards.

Flashcards: Special triangles

Two of a triangle's interior angles measure $30^{\circ}$ and $90^{\circ}$ , respectively. If this triangle's hypotenuse is $2\;\textup{in}$ long, what are the lengths of its other sides?

$\frac{\sqrt2}{2}\;\textup{in}\;\textup{and}\;\sqrt{3}\;\textup{in}$

$\frac{1}{2}\;\textup{in}\;\textup{and}\;\sqrt{2}\;\textup{in}$

$\sqrt3\;\textup{in}\;\textup{and}\;1\;\textup{in}$

$\sqrt2\;\textup{in}\;\textup{and}\;2\;\textup{in}$

$\frac{\sqrt3}{2}\;\textup{in}\;\textup{and}\;\sqrt{2}\;\textup{in}$

Report an Error Copyright Notice

Flashcards: Special triangles

Two of a triangle's interior angles measure $30^{\circ}$ and $90^{\circ}$ , respectively. If this triangle's hypotenuse is $2\;\textup{in}$ long, what are the lengths of its other sides?

Your answer:

$\frac{\sqrt2}{2}\;\textup{in}\;\textup{and}\;\sqrt{3}\;\textup{in}$

Your answer:

$\frac{1}{2}\;\textup{in}\;\textup{and}\;\sqrt{2}\;\textup{in}$

Your answer:

$\sqrt2\;\textup{in}\;\textup{and}\;2\;\textup{in}$

Your answer:

$\frac{\sqrt3}{2}\;\textup{in}\;\textup{and}\;\sqrt{2}\;\textup{in}$

Correct answer:

$\sqrt3\;\textup{in}\;\textup{and}\;1\;\textup{in}$

Explanation:

A triangle that has interior angles of $30^{\circ}$ and $90^{\circ}$ is necessarily a 30-60-90 triangle—a special right triangle. We can tell that the third angle about which we're not told anything has to be $60^{\circ}$ because a triangle's interior angles always sum to $180^{\circ}$ , allowing us to solve for the third angle like so:

$a+b+c=180^{\circ}$

$30^{\circ}+b+90^{\circ}=180^{\circ}$

$120^{\circ}+b=180^{\circ}$

$(120^{\circ}+b)-120^{\circ}=(180^{\circ})-120^{\circ}$

$b=60^{\circ}$

Since we know this triangle is a 30-60-90 triangle, we can use the special ratios that always hold true for this triangle's sides and angles to figure out the lengths of its other sides. The following ratio holds true for all 30-60-90 triangles, where the side in a fraction with a given angle is the side opposite that angle.

$\frac{30^{\circ}}{x}=\frac{60^{\circ}}{x\sqrt3}=\frac{90^{\circ}}{2x}$

We're told that the hypotenuse of our triangle has a length of $2\;\textup{in}$ . The hypotenuse is the triangle's longest side, so it will be located directly across from its largest angle. In this case, that angle is $90^{\circ}$ . So, we need to set equivalent to $2\;\textup{in}$ and solve for .

$x=\frac{2}{2}=1$

As you can see, for this particular triangle, . Using this information, we can now calculate the lengths of the other sides of the triangle. The side opposite the $30^{\circ}$ angle will be equal to inches; since , this side's length is $1\;\textup{in}$ . The side opposite the $60^{\circ}$ angle will be equal to $x\sqrt3\;\textup{in}$ . Substituting in into this expression, we find that this side has a length of $\sqrt{3}\;\textup{in}$ .

Thus, the correct answer is $\sqrt3\;\textup{in}\;\textup{and}\;1\;\textup{in}$ .

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)

View Tutors

Toni
Certified Tutor

University of West Georgia, Bachelor of Science, Early Childhood Education. Walden University, Doctor of Science, Urban Educa...

View Tutors

Kristine
Certified Tutor

Pennsylvania State University-Main Campus, Bachelor of Science, Accounting. Albany State University, Master of Science, Taxat...

View Tutors

Charlotte
Certified Tutor

University of North Carolina at Chapel Hill, Bachelor in Arts, Linguistics. University of North Carolina at Chapel Hill, Mast...

Popular Subjects

ACT Tutors in San Diego, French Tutors in San Diego, French Tutors in Los Angeles, LSAT Tutors in Miami, MCAT Tutors in Denver, Statistics Tutors in Los Angeles, LSAT Tutors in San Diego, Math Tutors in Dallas Fort Worth, Computer Science Tutors in Boston, Calculus Tutors in Los Angeles

Popular Courses & Classes

SAT Courses & Classes in Seattle, ISEE Courses & Classes in Atlanta, SSAT Courses & Classes in Washington DC, Spanish Courses & Classes in Seattle, GMAT Courses & Classes in Dallas Fort Worth, GRE Courses & Classes in San Diego, GMAT Courses & Classes in New York City, LSAT Courses & Classes in Miami, ISEE Courses & Classes in New York City, GMAT Courses & Classes in Boston

Popular Test Prep

LSAT Test Prep in Chicago, ACT Test Prep in Los Angeles, GMAT Test Prep in New York City, SAT Test Prep in New York City, SSAT Test Prep in Phoenix, ACT Test Prep in Atlanta, GRE Test Prep in Los Angeles, GMAT Test Prep in Dallas Fort Worth, ACT Test Prep in San Francisco-Bay Area, GRE Test Prep in San Diego

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Create an account to track your scores
and create your own practice tests:

All HiSET: Math Resources

Flashcards: Special triangles

Flashcards: Special triangles

Flashcards: Special triangles

Flashcards: Special triangles

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback:

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Create an account to track your scores and create your own practice tests:

All HiSET: Math Resources

Flashcards: Special triangles

Flashcards: Special triangles

Flashcards: Special triangles

Flashcards: Special triangles

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Create an account to track your scores
and create your own practice tests: