Call Now to Set Up Tutoring:

(888) 888-0446

SAT Math : How to find the length of the side of a right triangle

Study concepts, example questions & explanations for SAT Math

Create An Account

All SAT Math Resources

16 Diagnostic Tests 660 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

← Previous 1 2 Next →

Example Question #11 : How To Find The Length Of The Side Of A Right Triangle

Given $\bigtriangleup ABC$ with $m \angle A > m \angle B$ and $m \angle C = 90^{\circ }$ .

Which of the following could be the correct ordering of the lengths of the sides of the triangle?

I) AB > BC > AC

II) BC > AB > AC

III) BC > AC > AB

Possible Answers:

I or II only

II or III only

II only

I only

III only

Correct answer:

I only

Explanation:

Given two angles of unequal measure in a triangle, the side opposite the greater angle is longer than the side opposite the other angle. Since $m \angle A > m \angle B$ , it follows that BC > AC . Also, in a right triangle, the hypotenuse must be the longest side; in $\bigtriangleup ABC$ , since $\angle C$ is the right side, this hypotenuse is $\overline{AB}$ . It follows that AB > BC > AC , and that (I) is the only statement that can possibly be true.

Report an Error

Example Question #101 : Triangles

Triangle

$\left ( \bigtriangleup ABC \textup{ is a right triangle where } \angle B \textup{ is a right angle}\right)$

If $\angle A=30^{\circ}$ and $\overline{AB}=4$ , what is the length of $\overline{BC}$ ?

Possible Answers:

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

$\frac{4}{3}$

Correct answer:

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

Explanation:

AB is the leg adjacent to Angle A and BC is the leg opposite Angle A.

Since we have a $30^{\circ}-60^{\circ}-90^{\circ}$ triangle, the opposites sides of those angles will be in the ratio $x-x\sqrt{3}-2x$ .

Here, we know the side opposite the sixty degree angle. Thus, we can set that value equal to $x\sqrt{3}$ .

$4=x\sqrt{3}$

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

$\frac{4}{\sqrt{3}}\cdot \frac{\sqrt{3}}{\sqrt{3}}=x$

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

which also means

$\overline{BC}=\frac{4\sqrt{3}}{3}$

Report an Error

Example Question #112 : Sat Mathematics

A single-sided ladder is leaning against a wall. The angle between the end of the ladder that is on the ground and the ground itself is represented by $x^{\circ}$ . The ladder is sliding down the wall at a rate of 6 feet per second. If

$\sin x^{\circ}=\frac{3}{5}$

how many seconds does it take for the ladder to fall all the way to the ground? (The wall is a right angle to the ground.)

Possible Answers:

$1 \text{ second}$

$6 \text{ seconds}$

$1.1 \text{ seconds}$

$2.2 \text{ seconds}$

$0.5 \text{ seconds}$

Correct answer:

$0.5 \text{ seconds}$

Explanation:

The ladder leaning against the wall forms a right triangle. The hypotenuse of the triangle is 5 ft., the length of the ladder.

Because sin x= opposite/hypotenuse, sine of the angle is equal to the length of the side opposite the angle divided by the hypotenuse. In this case, the length of the side opposite the angle is h, the height of the end of the ladder that is touching the wall. Thus,

$\sin x^{\circ} = \frac{h}{5}$

Because we are told that

$\sin x^{\circ}=\frac{3}{5}$

we know that h=3. Therefore, 3 feet is the height of the ladder. If the ladder is falling at a rate of 6 feet per second, we can find the number of seconds it will take the ladder to hit the ground with the equation

h=6s

where h represents the height the ladder is falling from, and s represents the number of seconds it takes the ladder to fall. We can now solve for s:

$s=\frac{h}{6}$

$s=\frac{3}{6}=\frac{1}{2}=0.5$

It takes the ladder 0.5 seconds to fall to the ground.

Report an Error

Example Question #113 : Sat Mathematics

Right triangle 7

Refer to the provided figure. Give the length of $\overline{BC}$ .

Possible Answers:

$\frac{20}{3} \sqrt{2}$

$10\sqrt{3}$

$\frac{20}{3} \sqrt{3}$

$10\sqrt{2}$

Correct answer:

$10\sqrt{2}$

Explanation:

The figure shows a right triangle. The acute angles of a right triangle have measures whose sum is $90^{\circ }$ , so

$m \angle A+ m \angle C = 90^{\circ }$

Substituting $45^{\circ }$ for $m \angle C$ :

$m \angle A+ 45^{\circ } = 90^{\circ }$

$m \angle A= 45^{\circ }$

This makes $\bigtriangleup ABC$ a 45-45-90 triangle. By the 45-45-90 Triangle Theorem, the length of leg $\overline{BC}$ is equal to that of hypotenuse $\overline{AC}$ , the length of which is 20. Therefore,

$BC = \frac{AC}{\sqrt{2}} = \frac{20}{\sqrt{2}}$

Rationalize the denominator by multiplying both halves of the fraction by $\sqrt{2}$ :

$BC = \frac{20 \cdot \sqrt{2}}{\sqrt{2} \cdot \sqrt{2}} = \frac{20 \sqrt{2}}{2} = 10 \sqrt{2}$

Report an Error

← Previous 1 2 Next →

View SAT Mathematics Tutors

Liban
Certified Tutor

Emory University, Bachelor of Science, Mathematics/Economics.

View SAT Mathematics Tutors

Amanda
Certified Tutor

Seattle University, Current Undergrad Student, Applied Mathematics.

View SAT Mathematics Tutors

Chase
Certified Tutor

Western Governors University, Bachelor of Science, Mathematics.

All SAT Math Resources

16 Diagnostic Tests 660 Practice Tests Question of the Day Flashcards Learn by Concept

SAT Math Tutors in Top Cities:

Atlanta SAT Math Tutors, Austin SAT Math Tutors, Boston SAT Math Tutors, Chicago SAT Math Tutors, Dallas Fort Worth SAT Math Tutors, Denver SAT Math Tutors, Houston SAT Math Tutors, Kansas City SAT Math Tutors, Los Angeles SAT Math Tutors, Miami SAT Math Tutors, New York City SAT Math Tutors, Philadelphia SAT Math Tutors, Phoenix SAT Math Tutors, San Diego SAT Math Tutors, San Francisco-Bay Area SAT Math Tutors, Seattle SAT Math Tutors, St. Louis SAT Math Tutors, Tucson SAT Math Tutors, Washington DC SAT Math Tutors

Popular Courses & Classes

ISEE Courses & Classes in Washington DC, SAT Courses & Classes in Phoenix, MCAT Courses & Classes in Washington DC, LSAT Courses & Classes in Atlanta, SAT Courses & Classes in Washington DC, LSAT Courses & Classes in Los Angeles, GMAT Courses & Classes in New York City, MCAT Courses & Classes in Atlanta, ACT Courses & Classes in New York City, GRE Courses & Classes in San Francisco-Bay Area

Popular Test Prep

GRE Test Prep in Atlanta, ISEE Test Prep in San Francisco-Bay Area, ISEE Test Prep in Washington DC, GRE Test Prep in Washington DC, MCAT Test Prep in Los Angeles, SSAT Test Prep in Denver, ACT Test Prep in Phoenix, MCAT Test Prep in Seattle, ACT Test Prep in San Diego, ACT 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

SAT Math : How to find the length of the side of a right triangle

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #11 : How To Find The Length Of The Side Of A Right Triangle

Example Question #101 : Triangles

Example Question #112 : Sat Mathematics

Example Question #113 : Sat Mathematics

All SAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: