We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

ACT Math : Triangles

Study concepts, example questions & explanations for ACT Math

Create An Account

All ACT Math Resources

14 Diagnostic Tests 767 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #61 : Triangles

An airplane is 8 miles west and 15 miles south of its destination. Approximately how far is the plane from its destination, in miles?

Possible Answers:

$7\ miles$

$17\ miles$

$23\ miles$

$30\ miles$

Correct answer:

$17\ miles$

Explanation:

A right triangle can be drawn between the airplane and its destination.

Destination

15 miles Act_math_170_01 Airplane

8 miles

We can solve for the hypotenuse, x, of the triangle:

8² + 15² = x²

64 + 225 = x²

289 = x²

x = 17 miles

Report an Error

Example Question #501 : Geometry

An 8-foot-tall tree is perpendicular to the ground and casts a 6-foot shadow. What is the distance, to the nearest foot, from the top of the tree to the end of the shadow?

Possible Answers:

$\dpi{100} \small 4$

$\dpi{100} \small 10$

$\dpi{100} \small 5$

$\dpi{100} \small 8$

$\dpi{100} \small 6$

Correct answer:

$\dpi{100} \small 10$

Explanation:

In order to find the distance from the top of the tree to the end of the shadow, draw a right triangle with the height(tree) labeled as 8 and base(shadow) labeled as 6:

Screen_shot_2013-08-16_at_12.34.40_am

From this diagram, you can see that the distance being asked for is the hypotenuse. From here, you can either use the Pythagorean Theorem:

$\dpi{100} \small a^{2}+b^{2}=c^{2}$

or you can notice that this is simililar to a 3-4-5 triangle. Since the lengths are just increased by a factor of 2, the hypotenuse that is normally 5 would be 10.

8^2+6^2=c^2

64+36=c^2

100=c^2

10=c

Report an Error

Example Question #62 : Triangles

Screen_shot_2013-03-18_at_10.21.29_pm

In the figure above, ABCD is a square and is three times the length of . What is the area of ABCD ?

Possible Answers:

100

Correct answer:

Explanation:

Assigning the length of ED the value of x, the value of AE will be 3x. That makes the entire side AD equal to 4x. Since the figure is a square, all four sides will be equal to 4x. Also, since the figure is a square, then angle A of triangle ABE is a right angle. That gives triangle ABE sides of 3x, 4x and 10. Using the Pythagorean theorem:

(3x)² + (4x)² = 10²

9x² + 16x² = 100

25x² = 100

x² = 4

x = 2

With x = 2, each side of the square is 4x, or 8. The area of a square is length times width. In this case, that's 8 * 8, which is 64.

Report an Error

Example Question #63 : Triangles

The hypotenuse is the diameter of the circle. Find the area of the circle above.

Possible Answers:

$6.75\pi$

$6.25\pi$

$5.5\pi$

$5\pi$

$6.5\pi$

Correct answer:

$6.25\pi$

Explanation:

Using the Pythagorean Theorem, we can find the length of the hypotenuse:

$3^{2}+4^{2}=5^{2}$ .

Therefore the hypotenuse has length 5.

The area of the circle is $\pi r^{2}=\pi \cdot 2.5^{2}=6.25\pi$

Report an Error

Example Question #504 : Geometry

Find the length of the hypotenuse.

Triangle_4_14_c

Note: This is a right triangle.

Possible Answers:

$4\sqrt{53}$

$\sqrt{91}$

$2\sqrt{53}$

Correct answer:

$2\sqrt{53}$

Explanation:

To find the length of this hypotenuse, we need to use the Pythagorean Theorem:

c^2=a^2+b^2 , where a and b are the legs and c is the hypotenuse.

Here, c is our missing hypotenuse length, a = 4 ,and b = 14.

Plug these values in and solve for c:

c^2=4^2+14^2=16+196=212

$c=\sqrt{212}=\sqrt{4 \cdot 53}=\sqrt{4}\sqrt{53}=2\sqrt{53}$

Report an Error

Example Question #505 : Geometry

Side in the triangle below (not to scale) is equal to . Side is equal to . What is the length of side ?

Right_triangle_with_labeled_sides

Possible Answers:

$\ 146$

$\sqrt{135}$

$\sqrt{146}$

Correct answer:

$\sqrt{146}$

Explanation:

Use the Pythagorean Theorem: $a^{2}+b^{2}=c^{2}$ , where a and b are the legs and c is the hypotenuse.

We know and , so we can plug them in to solve for c:

$5^{2}+11^{2}=c^{2}$

$25+121=c^{2}$

$146=c^{2}$

$c=\sqrt{146}$

Report an Error

Example Question #48 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Dan drives 5 miles north and then 8 miles west to get to school. If he walks, he can take a direct path from his house to the school, cutting down the distance. How long is the path from Dan's house to his school?

Possible Answers:

13 miles

4.36 miles

19 miles

9.43 miles

89 miles

Correct answer:

9.43 miles

Explanation:

We are really looking for the hypotenuse of a triangle that has legs of 5 miles and 8 miles.

Apply the Pythagorean Theorem:

a² + b² = c²

25 + 64 = c²

89 = c²

c = 9.43 miles

Report an Error

Example Question #506 : Geometry

What is the hypotenuse of a right triangle with side lengths and ?

Possible Answers:

Correct answer:

Explanation:

The Pythagorean Theorem states that . This question gives us the values of and , and asks us to solve for .

Take and and plug them into the equation as and :

$12^{2}+16^{2}=c^{2}$

Now we can start solving for :

$144+256=c^{2}$

$400=c^{2}$

$\sqrt{400}=\sqrt{c^{2}}$

20=c

The length of the hypotenuse is .

Report an Error

Example Question #71 : Right Triangles

One leg of a triangle measures 12 inches. Which of the following could be the length of the other leg if the hypotenuse is an integer length?

Possible Answers:

$15\ inches$

$16\ inches$

$20\ inches$

$12\ inches$

$4\ inches$

Correct answer:

$16\ inches$

Explanation:

By the Pythagorean Theorem, if is the hypotenuse and and are the legs, $c = \sqrt{a^{2}+b^{2}}}$ .

Set a=12 , the known leg, and rewrite the above as:

$c = \sqrt{12^{2}+b^{2}}}$

$c = \sqrt{144+b^{2}}}$

We can now substitute each of the five choices for ; the one which yields a whole number for is the correct answer choice.

b=4 :

$c = \sqrt{144+4^{2}}} = \sqrt{144+16}} =\sqrt{160}=12.64...$

b=12 :

$c = \sqrt{144+12^{2}}} = \sqrt{144+144}} =\sqrt{288}=16.97...$

b=15 :

$c = \sqrt{144+15^{2}}} = \sqrt{144+225}} =\sqrt{369}=19.20...$

b=16 :

$c = \sqrt{144+16^{2}}} = \sqrt{144+256}} =\sqrt{400}=20$

b=20 :

$c = \sqrt{144+20^{2}}} = \sqrt{144+400}} =\sqrt{544}=23.32...$

The only value of which yields a whole number for the hypotenuse is 16, so this is the one we choose.

Report an Error

Example Question #72 : Right Triangles

Find the perimeter of the polygon.

Possible Answers:

Correct answer:

Explanation:

Divide the shape into a rectangle and a right triangle as indicated below.

Find the hypotenuse of the right triangle with the Pythagorean Theorem, a^2 + b^2 = c^2 , where and are the legs of the triangle and is its hypotenuse.

(8)^2+(6)^2 = c^2

100 = c^2

$\sqrt{100} = \sqrt{c^2}$

c =10

This is our missing length.

Now add the sides of the polygon together to find the perimeter:

20 + 10 + 26 + 8 = 64

Report an Error

View ACT Math Tutors

Chukwudi
Certified Tutor

University of Nigeria, Nsukka., Bachelor of Science, Biochemistry. African University of Science and Technology., Master of S...

View ACT Math Tutors

Jhemson
Certified Tutor

Batangas State University, Doctor of Philosophy, Mathematics.

View ACT Math Tutors

Dalton
Certified Tutor

University of Massachusetts Amherst, Doctor of Philosophy, Mathematics.

All ACT Math Resources

14 Diagnostic Tests 767 Practice Tests Question of the Day Flashcards Learn by Concept

ACT Math Tutors in Top Cities:

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

Popular Courses & Classes

MCAT Courses & Classes in Los Angeles, ISEE Courses & Classes in Seattle, SSAT Courses & Classes in Seattle, SAT Courses & Classes in Boston, SAT Courses & Classes in Dallas Fort Worth, LSAT Courses & Classes in Dallas Fort Worth, GMAT Courses & Classes in New York City, ACT Courses & Classes in San Diego, MCAT Courses & Classes in Boston, ISEE Courses & Classes in Los Angeles

Popular Test Prep

LSAT Test Prep in Los Angeles, SAT Test Prep in Seattle, SSAT Test Prep in Denver, LSAT Test Prep in Miami, MCAT Test Prep in Philadelphia, MCAT Test Prep in Dallas Fort Worth, SAT Test Prep in New York City, ACT Test Prep in San Diego, LSAT Test Prep in San Diego, GMAT Test Prep in Seattle

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

ACT Math : Triangles

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #61 : Triangles

Example Question #501 : Geometry

Example Question #62 : Triangles

Example Question #63 : Triangles

Example Question #504 : Geometry

Example Question #505 : Geometry

Example Question #48 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #506 : Geometry

Example Question #71 : Right Triangles

Example Question #72 : Right Triangles

All ACT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: