We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

ISEE Upper Level Math : How to find the height of an eqilateral triangle

Study concepts, example questions & explanations for ISEE Upper Level Math

Create An Account

All ISEE Upper Level Math Resources

6 Diagnostic Tests 244 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #11 : Equilateral Triangles

The length of one side of an equilateral triangle is 4 centimeters. Give the height (altitude) of the triangle.

Possible Answers:

$4\sqrt{3}\ cm$

$3\sqrt{3}\ cm$

$2\sqrt{3}\ cm$

$4\ cm$

$3\ cm$

Correct answer:

$2\sqrt{3}\ cm$

Explanation:

$Area=\frac{1}{2}absinC$ ,

where and are the lengths of two sides and is the corresponding angle.

In an equilateral triangle, all of the sides have the same length, and all three angles are $60^{\circ}$ .

$Area=\frac{1}{2}absinC=\frac{1}{2}\times 4\times 4\times sin60^{\circ}$

$sin60^{\circ}=\frac{\sqrt{3}}{2}\Rightarrow Area=\frac{1}{2}\times 4\times 4\times \frac{\sqrt{3}}{2}=4\sqrt{3}\ cm^2$

Now plug this area into the alternate formula for the area of the triangle and solve for the height:

$Area =\frac{bh}2{}\Rightarrow 4\sqrt{3}=\frac{4\times h}{2}\Rightarrow h=2\sqrt{3}\ cm$

Report an Error

Example Question #71 : Triangles

The height of the equilateral triangle below is 5 centimeters. Give the perimeter of the triangle.

Possible Answers:

$\frac{8}{3}\ cm$

$\frac{8\sqrt{3}}{3}\ cm$

$4\ cm$

$\frac{4\sqrt{3}}{3}\ cm$

$8\ cm$

Correct answer:

$\frac{8\sqrt{3}}{3}\ cm$

Explanation:

In an equilateral triangle all of the sides have the same length, so all we need to do is find the length of one side.

We know that, in an equilateral triangle, all three angles measure $60^{\circ}$ .

$sin\angle A=\frac{h}{AB}=\frac{h}{c}$

$sin\angle A=\frac{h}{c}\Rightarrow sin60^{\circ}=\frac{4}{c}\Rightarrow \frac{\sqrt{3}}{2}=\frac{4}{c}\Rightarrow c=\frac{8}{\sqrt{3}}=\frac{8\sqrt{3}}{3} \ cm$

Report an Error

View Tutors

Nishana
Certified Tutor

University Of Calicut, Master's/Graduate, Physics.

View Tutors

Angeles
Certified Tutor

University of Central Florida, Bachelor of Science, Biomedical Sciences. University of Central Florida, Master of Science, Bi...

View Tutors

Sumit
Certified Tutor

Calcutta University, Bachelor of Science, Mathematics. Indian Statistical Institute, Master of Science, Mathematics.

All ISEE Upper Level Math Resources

6 Diagnostic Tests 244 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Physics Tutors in Phoenix, Math Tutors in San Francisco-Bay Area, Biology Tutors in San Diego, LSAT Tutors in Los Angeles, Biology Tutors in Washington DC, Calculus Tutors in Boston, Computer Science Tutors in Phoenix, Physics Tutors in Atlanta, Chemistry Tutors in Washington DC, SAT Tutors in Washington DC

Popular Courses & Classes

LSAT Courses & Classes in New York City, MCAT Courses & Classes in San Diego, GRE Courses & Classes in Philadelphia, MCAT Courses & Classes in Atlanta, MCAT Courses & Classes in Philadelphia, ISEE Courses & Classes in New York City, ACT Courses & Classes in Houston, ISEE Courses & Classes in Washington DC, ISEE Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in San Francisco-Bay Area

Popular Test Prep

SSAT Test Prep in Los Angeles, ACT Test Prep in Houston, GRE Test Prep in Washington DC, GRE Test Prep in San Francisco-Bay Area, ACT Test Prep in San Diego, SAT Test Prep in Atlanta, MCAT Test Prep in Seattle, GRE Test Prep in Chicago, GRE Test Prep in Miami, ISEE Test Prep in New York City

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)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

ISEE Upper Level Math : How to find the height of an eqilateral triangle

Study concepts, example questions & explanations for ISEE Upper Level Math

All ISEE Upper Level Math Resources

Example Questions

Example Question #11 : Equilateral Triangles

Example Question #71 : Triangles

All ISEE Upper Level Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: