Call Now to Set Up Tutoring:

(888) 888-0446

SAT Math : Right Triangles

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

Example Question #3 : How To Find The Length Of The Side Of A Right Triangle

Bob the Helicopter is at 30,000 ft. above sea level, and as viewed on a map his airport is 40,000 ft. away. If Bob travels in a straight line to his airport at 250 feet per second, how many minutes will it take him to arrive?

Possible Answers:

4 hours and 0 minutes

3 minutes and 50 seconds

2 hours and 30 minutes

3 minutes and 20 seconds

1 hour and 45 minutes

Correct answer:

3 minutes and 20 seconds

Explanation:

Draw a right triangle with a height of 30,000 ft. and a base of 40,000 ft. The hypotenuse, or distance travelled, is then 50,000ft using the Pythagorean Theorem. Then dividing distance by speed will give us time, which is 200 seconds, or 3 minutes and 20 seconds.

Report an Error

Example Question #4 : How To Find The Length Of The Side Of A Right Triangle

A right triangle has two sides, 9 and x, and a hypotenuse of 15. What is x?

Possible Answers:

Correct answer:

Explanation:

We can use the Pythagorean Theorem to solve for x.

9² + x² = 15²

81 + x² = 225

x² = 144

x = 12

Report an Error

Example Question #5 : How To Find The Length Of The Side Of A Right Triangle

The area of a right traingle is 42. One of the legs has a length of 12. What is the length of the other leg?

Possible Answers:

$6$

$7$

$11$

$9$

$5$

Correct answer:

$7$

Explanation:

$Area= \frac{1}{2}\times base\times height$

$42=\frac{1}{2}\times base\times 12$

$42=6\times base$

$base=7$

Report an Error

Example Question #6 : How To Find The Length Of The Side Of A Right Triangle

Solve for x.

Possible Answers:

Correct answer:

Explanation:

Use the Pythagorean Theorem. Let a = 8 and c = 10 (because it is the hypotenuse)

$\small a^2+x^2=c^2$

$\small 8^2+x^2=10^2$

$\small 64+x^2=100$

$\small x^2=100-64=36$

$\small x=6$

Report an Error

Example Question #2 : How To Find The Length Of The Side Of A Right Triangle

Solve each problem and decide which is the best of the choices given.

If $sin x =\frac{12}{13}$ , what is tan (x) ?

Possible Answers:

$tan(x)=\frac{12}{5}$

$tan(x)=\frac{5}{12}$

$tan(x)=\frac{5}{13}$

$tan(x)=\frac{12}{13}$

$tan(x)=\frac{13}{12}$

Correct answer:

$tan(x)=\frac{12}{5}$

Explanation:

This is a 5-12-13 triangle. We can find the value of the other leg by using the Pythagorean Theorem.

Remembering that

$sin=\frac{opposite}{hypotenuse}$ .

Thus,

a^2+12^2=13^2

a^2+144=169

a^2=25

a=5 .

If $sin(x)=\frac{12}{13}$ , you know the adjacent side is .

Thus, making

$tan(x)=\frac{opposite}{adjacent}=\frac{12}{5}$ because tangent is opposite/adjacent.

Report an Error

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 only

III only

I only

II or 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 #111 : Sat Mathematics

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 #12 : How To Find The Length Of The Side Of A Right Triangle

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:

$1 \text{ second}$

$6 \text{ seconds}$

$2.2 \text{ seconds}$

$0.5 \text{ seconds}$

$1.1 \text{ seconds}$

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 #13 : How To Find The Length Of The Side Of A Right Triangle

Right triangle 7

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

Possible Answers:

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

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

$10\sqrt{2}$

$10\sqrt{3}$

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

Example Question #1 : Right Triangles

Triangles

In the figure above, line segments DC and AB are parallel. What is the perimeter of quadrilateral ABCD?

Possible Answers:

Correct answer:

Explanation:

Because DC and AB are parallel, this means that angles CDB and ABD are equal. When two parallel lines are cut by a transversal line, alternate interior angles (such as CDB and ABD) are congruent.

Now, we can show that triangles ABD and BDC are similar. Both ABD and BDC are right triangles. This means that they have one angle that is the same—their right angle. Also, we just established that angles CDB and ABD are congruent. By the angle-angle similarity theorem, if two triangles have two angles that are congruent, they are similar. Thus triangles ABD and BDC are similar triangles.

We can use the similarity between triangles ABD and BDC to find the lengths of BC and CD. The length of BC is proportional to the length of AD, and the length of CD is proportional to the length of DB, because these sides correspond.

We don’t know the length of DB, but we can find it using the Pythagorean Theorem. Let a, b, and c represent the lengths of AD, AB, and BD respectively. According to the Pythagorean Theorem:

a² + b²= c²

15² + 20²= c²

625 = c²

c = 25

The length of BD is 25.

Similar_triangles

We now have what we need to find the perimeter of the quadrilateral.

Perimeter = sum of the lengths of AB, BC, CD, and DA.

Perimeter = 20 + 18.75 + 31.25 + 15 = 85

The answer is 85.

Report an Error

View SAT Mathematics Tutors

Joy
Certified Tutor

Boston University, Bachelor in Arts, Conservation Biology.

View SAT Mathematics Tutors

Thomas
Certified Tutor

Michigan State University, Bachelor in Arts, History. Central Michigan University, Doctor of Philosophy, History.

View SAT Mathematics Tutors

Kelly
Certified Tutor

CUNY Hunter College, Bachelor in Arts, Economics.

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

GRE Courses & Classes in Washington DC, Spanish Courses & Classes in Boston, MCAT Courses & Classes in San Francisco-Bay Area, SAT Courses & Classes in Boston, MCAT Courses & Classes in Phoenix, LSAT Courses & Classes in Philadelphia, MCAT Courses & Classes in Denver, SSAT Courses & Classes in New York City, ACT Courses & Classes in Philadelphia, Spanish Courses & Classes in Seattle

Popular Test Prep

MCAT Test Prep in Houston, ISEE Test Prep in Seattle, ISEE Test Prep in Denver, GMAT Test Prep in Chicago, GRE Test Prep in Boston, ACT Test Prep in Atlanta, LSAT Test Prep in Philadelphia, MCAT Test Prep in Miami, LSAT Test Prep in New York City, SAT Test Prep in Boston

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 : Right Triangles

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #3 : How To Find The Length Of The Side Of A Right Triangle

Example Question #4 : How To Find The Length Of The Side Of A Right Triangle

Example Question #5 : How To Find The Length Of The Side Of A Right Triangle

Example Question #6 : How To Find The Length Of The Side Of A Right Triangle

Example Question #2 : How To Find The Length Of The Side Of A Right Triangle

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

Example Question #111 : Sat Mathematics

Example Question #12 : How To Find The Length Of The Side Of A Right Triangle

Example Question #13 : How To Find The Length Of The Side Of A Right Triangle

Example Question #1 : Right Triangles

All SAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: