Call Now to Set Up Tutoring:

(888) 888-0446

High School Math : Triangles

Study concepts, example questions & explanations for High School Math

Create An Account

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #19 : How To Find The Length Of The Side Of A Right Triangle

Given a right triangle, solve for the missing leg if one leg is 12 and the hypotenuse is 13.

Possible Answers:

17.69

Correct answer:

Explanation:

Since the traingle is a right traingle, we can use the Pythagorean Theorem to solve for the missing leg:

a^2 + b^2 = c^2

a=12 and the hypotenuse c=13

(12)^2 + b^2 = (13)^2

b^2 = (13)^2- (12)^2

b^2 = 169- 144

b^2 = 25

b = 5

Report an Error

Example Question #21 : How To Find The Length Of The Side Of A Right Triangle

Points $\dpi{100} \small A$ , $\dpi{100} \small B$ , and $\dpi{100} \small C$ are collinear (they lie along the same line). $\angle ACD = 90^{\circ}$ , $\angle CAD=30^{\circ}$ , $\angle CBD=60^{\circ}$ , $\overline{AD}=4$

Find the length of segment $\overline{BD}$ .

Possible Answers:

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

$2\sqrt{3}$

$2$

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

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

Correct answer:

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

Explanation:

The length of segment $\overline{BD}$ is $\frac{4\sqrt{3}}{3}$

Note that triangles $\dpi{100} \small ACD$ and $\dpi{100} \small BCD$ are both special, 30-60-90 right triangles. Looking specifically at triangle $\dpi{100} \small ACD$ , because we know that segment $\overline{AD}$ has a length of 4, we can determine that the length of segment $\overline{CD}$ is 2 using what we know about special right triangles. Then, looking at triangle $\dpi{100} \small BCD$ now, we can use the same rules to determine that segment $\overline{BD}$ has a length of $\frac{4}{\sqrt{3}}$

which simplifies to $\frac{4\sqrt{3}}{3}$ .

Report an Error

Example Question #1 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

$\textup{What is the length of the hypotenuse of a right triangle with legs of lengths 10 and 15?}$

Possible Answers:

$6\sqrt{13}$

$13\sqrt{5}$

$5\sqrt{13}$

Correct answer:

$5\sqrt{13}$

Explanation:

$\textup{Pythagorean Theorum: }a^{2}+b^{2}= c^{2}\;\;\;\;\;\;10^{2}+15^{2}=c^{2}$

$100+225=c^{2}\;\;\;\;325=c^{2}\;\;\;\;\;\sqrt{325}=c\;\;\;\;\sqrt{25}\times\sqrt{13}=c$

$5\sqrt{13}=c$

Report an Error

Example Question #1 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Rt_triangle_letters

If angle $c=90^\circ$ , Y=3 and Z=4 , what is the value of ?

Possible Answers:

12.5

Correct answer:

Explanation:

Once we see that $c=90^\circ$ , we know that we're working with a right triangle and that will be the hypotenuse.

At this point we can use the Pythaogrean theorem ( a^2+b^2=c^2 ) or, in this case: Y^2+Z^2=X^2 .

Plug in our given values to solve:

Y^2+Z^2=X^2

3^2+4^2=X^2

9+16=X^2

25=X^2

$\sqrt{25}=\sqrt{X^2}$

5=X

Report an Error

Example Question #1 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Rt_triangle_letters

If angle $c=90^\circ$ , X = 13 and Y = 12 , what is the value of ?

Possible Answers:

17.69

144

169

Correct answer:

Explanation:

Once we see that $c=90^\circ$ , we know we're working with a right triangle and that will be the hypotenuse.

At this point we can use the Pythaogrean theorem ( a^2+b^2=c^2 ) or, in this case: Y^2+Z^2=X^2 .

Plug in our given values to solve:

Y^2+Z^2=X^2

12^2+Z^2=13^2

144+Z^2=169

Subtract 144 from both sides:

Z^2=25

$\sqrt{Z^2}=\sqrt{25}$

Z=5

Report an Error

Example Question #4 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

A right triangle has legs of and . What is the hypotenuse?

Possible Answers:

$5\sqrt{5}$

$\sqrt{5}$

$5\sqrt{2}$

Correct answer:

$5\sqrt{2}$

Explanation:

To solve this problem, use the Pythagorean theorem: the sum of the square of the legs equals the square of the hyoptenuse or, mathematically, a^2+b^2=c^2 .

Plug in our given values.

a^2+b^2=c^2

5^2+5^2=c^2

25+25=c^2

50=c^2

$\sqrt{50}=\sqrt{c^2}$

is not a perfect square, but let's see if we can find a factor that is a perfect square.

$\sqrt{25*2}=\sqrt{c^2}$

IS a perfect square, so we can simplify!

$\sqrt{25}*\sqrt{2}=\sqrt{c^2}$

$5*\sqrt2=c$

$5\sqrt{2}=c$

This is going to be true of all isoceles right triangles: the pattern will always be $x:x:x\sqrt{2}$ .

Report an Error

Example Question #2 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

A right triangle has legs of and . What is the hypotenuse?

Possible Answers:

$2\sqrt{2}$

$4\sqrt{2}$

Correct answer:

$4\sqrt{2}$

Explanation:

To solve this problem, use the Pythagorean theorem: the sum of the square of the legs equals the square of the hyoptenuse or, mathematically, a^2+b^2=c^2 .

Plug in our given values.

a^2+b^2=c^2

4^2+4^2=c^2

16+16=c^2

32=c^2

$\sqrt{32}=\sqrt{c^2}$

is not a perfect square, but let's see if we can find a factor that is a perfect square.

$\sqrt{16*2}=\sqrt{c^2}$

IS a perfect square, so we can simplify!

$\sqrt{16}*\sqrt{2}=\sqrt{c^2}$

$4*\sqrt2=c$

$4\sqrt{2}=c$

Report an Error

Example Question #3 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Solve for :

Question_12

Possible Answers:

x=12

$x=6\sqrt2$

$x=9\sqrt2$

x=9

Correct answer:

$x=6\sqrt2$

Explanation:

Solve for using the Pythagorean Theorem:

c^2=a^2+b^2

x=c

x^2=6^2+6^2=36+36=72

$\sqrt{x^2}=\sqrt{72}$

$x=\sqrt{36}\times \sqrt2$

$x=6\sqrt2$

Report an Error

Example Question #1 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Trig_id

If o=10ft and a=17ft , how long is side ?

Possible Answers:

19.3ft

Not enough information to solve

19.7 ft

17.9ft

18ft

Correct answer:

19.7 ft

Explanation:

This problem is solved using the Pythagorean theorem $(a^{2}+b^{2}=c^{2})$ . In this formula and are the legs of the right triangle while is the hypotenuse.

Using the labels of our triangle we have:

$o^{2}+a^{2}=h^{2}$

$\dpi{100} h^{2}=(10ft)^{2} +(17ft)^{2}$

$h^{2}=100ft^{2}+289ft^{2}$

$h=\sqrt{389ft^{2}}$

$\rightarrow 19.7 ft$

Report an Error

Example Question #1 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

If one of the short sides of a 45-45-90 triangle equals 5, how long is the hypotenuse?

Possible Answers:

√15

√10

5√2

Correct answer:

5√2

Explanation:

Using the Pythagorean theorem, x² + y² = h². And since it is a 45-45-90 triangle the two short sides are equal. Therefore 5² + 5² = h². Multiplied out 25 + 25 = h².

Therefore h² = 50, so h = √50 = √2 * √25 or 5√2.

Report an Error

View Tutors

Nicole
Certified Tutor

Liberty University, Bachelor of Science, Psychology. Liberty University, Master of Arts, Mental Health Counseling.

View Tutors

Jeremy
Certified Tutor

University of Illinois at Chicago, Bachelor of Science, Physics.

View Tutors

Makayla
Certified Tutor

Highline Community College, Associate in Arts, Arts, General. Washington State University, Bachelor of Science, International...

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

GMAT Tutors in Seattle, MCAT Tutors in Houston, Chemistry Tutors in New York City, Math Tutors in Miami, Calculus Tutors in Boston, GMAT Tutors in Philadelphia, English Tutors in Los Angeles, Math Tutors in Houston, ISEE Tutors in San Diego, Algebra Tutors in Dallas Fort Worth

Popular Courses & Classes

Spanish Courses & Classes in Los Angeles, SAT Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in Denver, ISEE Courses & Classes in Denver, ISEE Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in Miami, ISEE Courses & Classes in Dallas Fort Worth, MCAT Courses & Classes in Houston, ACT Courses & Classes in Houston, ISEE Courses & Classes in Houston

Popular Test Prep

GMAT Test Prep in New York City, ACT Test Prep in Dallas Fort Worth, MCAT Test Prep in San Francisco-Bay Area, GMAT Test Prep in Miami, LSAT Test Prep in Washington DC, SSAT Test Prep in Washington DC, MCAT Test Prep in Seattle, ISEE Test Prep in Phoenix, ISEE Test Prep in Houston, SAT Test Prep in Philadelphia

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

High School Math : Triangles

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #19 : How To Find The Length Of The Side Of A Right Triangle

Example Question #21 : How To Find The Length Of The Side Of A Right Triangle

Example Question #1 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #1 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #1 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #4 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #2 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #3 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #1 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #1 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

All High School Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: