Call Now to Set Up Tutoring:

(888) 888-0446

PSAT Math : Plane Geometry

Study concepts, example questions & explanations for PSAT Math

Create An Account

All PSAT Math Resources

10 Diagnostic Tests 421 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

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 #1 : 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:

$7$

$9$

$6$

$11$

$5$

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

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:

$\frac{4}{3}$

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

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 #81 : Triangles

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 #462 : Geometry

Right_triangle

Note: Figure NOT drawn to scale.

Refer to the above diagram. Evaluate .

Possible Answers:

$M = 1\frac{5}{12}$

$M = 1\frac{12}{13}$

$M = 2\frac{1}{12}$

$M = 1\frac{5}{13}$

$M = 2\frac{5}{13}$

Correct answer:

$M = 1\frac{12}{13}$

Explanation:

The altitude perpendicular to the hypotenuse of a right triangle divides that triangle into two smaller triangles similar to each other and the large triangle. Therefore, the sides are in proportion. The hypotenuse of the triangle is equal to

$\sqrt{5^{2}+12^{2}} = \sqrt{25+144} = \sqrt{169} =13$

Therefore, we can set up, and solve for in, a proportion statement involving the shorter side and hypotenuse of the large triangle and the larger of the two smaller triangles:

$\frac{M}{5} = \frac{5}{13}$

$\frac{M}{5} \cdot 5 = \frac{5}{13} \cdot 5$

$M = \frac{25}{13} = 1\frac{12}{13}$

Report an Error

Example Question #11 : Right Triangles

What is the hypotenuse of a right triangle with sides 5 and 8?

Possible Answers:

5√4

8√13

√89

Correct answer:

√89

Explanation:

Because this is a right triangle, we can use the Pythagorean Theorem which says a² + b² = c², or the squares of the two sides of a right triangle must equal the square of the hypotenuse. Here we have a = 5 and b = 8.

a² + b² = c²

5² + 8² = c²

25 + 64 = c²

89 = c²

c = √89

Report an Error

Example Question #14 : Triangles

Trig_id

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

Possible Answers:

18ft

Not enough information to solve

17.9ft

19.3ft

19.7 ft

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 #21 : Right Triangles

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

Possible Answers:

5√2

√15

√10

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

Example Question #41 : Geometry

The height of a right circular cylinder is 10 inches and the diameter of its base is 6 inches. What is the distance from a point on the edge of the base to the center of the entire cylinder?

Possible Answers:

None of the other answers

√(34)

√(43)/2

3π/4

4π/5

Correct answer:

√(34)

Explanation:

The best thing to do here is to draw diagram and draw the appropiate triangle for what is being asked. It does not matter where you place your point on the base because any point will produce the same result. We know that the center of the base of the cylinder is 3 inches away from the base (6/2). We also know that the center of the cylinder is 5 inches from the base of the cylinder (10/2). So we have a right triangle with a height of 5 inches and a base of 3 inches. So using the Pythagorean Theorem 3²+ 5²= c². 34 = c², c = √(34).

Report an Error

Example Question #42 : Geometry

A right triangle with sides A, B, C and respective angles a, b, c has the following measurements.

Side A = 3in. Side B = 4in. What is the length of side C?

Possible Answers:

Correct answer:

Explanation:

The correct answer is 5. The pythagorean theorem states that a²+ b²= c². So in this case 3²+ 4²= C². So C²= 25 and C = 5. This is also an example of the common 3-4-5 triangle.

Report an Error

View PSAT Mathematics Tutors

Darian
Certified Tutor

University of North Texas, Current Undergrad Student, English.

View PSAT Mathematics Tutors

Reza
Certified Tutor

University of Sherbrooke, Doctor of Philosophy, Mathematics. University of Manitoba, Master of Science, Mathematics.

View PSAT Mathematics Tutors

Vanshika
Certified Tutor

Rutgers University-New Brunswick, Bachelor of Science, Economics.

All PSAT Math Resources

10 Diagnostic Tests 421 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Statistics Tutors in Phoenix, ISEE Tutors in Houston, MCAT Tutors in Denver, Spanish Tutors in Dallas Fort Worth, MCAT Tutors in Philadelphia, SSAT Tutors in Chicago, GMAT Tutors in Boston, ACT Tutors in Philadelphia, Algebra Tutors in Philadelphia, Physics Tutors in Washington DC

Popular Courses & Classes

LSAT Courses & Classes in Chicago, LSAT Courses & Classes in Los Angeles, ACT Courses & Classes in Chicago, ACT Courses & Classes in Phoenix, LSAT Courses & Classes in Atlanta, MCAT Courses & Classes in Seattle, SSAT Courses & Classes in Denver, Spanish Courses & Classes in Houston, Spanish Courses & Classes in San Diego, GMAT Courses & Classes in Boston

Popular Test Prep

GRE Test Prep in Denver, ISEE Test Prep in Houston, SAT Test Prep in San Francisco-Bay Area, SSAT Test Prep in New York City, MCAT Test Prep in Los Angeles, LSAT Test Prep in Los Angeles, ACT Test Prep in Chicago, ACT Test Prep in Phoenix, ISEE Test Prep in Denver, SSAT Test Prep in Chicago

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

PSAT Math : Plane Geometry

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

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

Example Question #1 : How To Find The Length Of The Side Of A Right Triangle

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

Example Question #81 : Triangles

Example Question #462 : Geometry

Example Question #11 : Right Triangles

Example Question #14 : Triangles

Example Question #21 : Right Triangles

Example Question #41 : Geometry

Example Question #42 : Geometry

All PSAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: