Call Now to Set Up Tutoring:

(888) 888-0446

ACT Math : ACT Math

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 #131 : Geometry

A right triangle has legs of length 20cm and 99 cm , what is the length of the hypotenuse?

Possible Answers:

10,201 cm

119 cm

$\sqrt{119}$

104cm

101 cm

Correct answer:

101 cm

Explanation:

To find the hypotenuse of a right triangle, use the Pythagorean Theorem and plug the leg values in for and :
$\\a^2 + b^2 = c^2 \\ \newline 20^2 + 99^2 = c^2 \\ \newline 10,201 = c^2 \\ \\ \sqrt{10,201}=\sqrt{c^2}\\ \newline 101 = c$

Report an Error

Example Question #51 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

A right triangle has a base of six and a height of eight. Using this information find the hypotenuse.

Possible Answers:

100

Correct answer:

Explanation:

This question calls for us to use the Pythagorean Theorem. This theorem has a formula of

a^2+b^2=c^2

where a and b are the sides of a right triangle, adjacent to the right angle, and c is the hypotenuse.

Given our information

$\\6^2+8^2=c^2\\ =36+64=100\\c=\sqrt{100}=10$ .

Report an Error

Example Question #52 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

A right triangle has a base of seven and a height of twelve. Using this information find the hypotenuse.

Possible Answers:

$\sqrt{19}$

$\sqrt{17}$

193

$\sqrt{193}$

Correct answer:

$\sqrt{193}$

Explanation:

This question calls for us to use the Pythagorean Theorem. This theorem has a formula of

a^2+b^2=c^2

where a and b are the sides of a right triangle, adjacent to the right angle, and c is the hypotenuse.

Given our information

$\\7^2+12^2=c^2\\=49+144=193\\c=\sqrt{193}$ .

Report an Error

Example Question #132 : Geometry

Marcus Absent is marking out some lines for a large canvas tent. He paces out $15\textup{ feet}$ to the north, places a peg, then turns east and paces another $25\textup{ feet}$ to place another peg. Stopping, he realizes he has forgotten the other pegs, so he makes a beeline for his original starting point.

How many $\textup{ feet}$ does Marcus travel to get back to the pegs?

Possible Answers:

$5\sqrt{34}\textup{ feet}$

$\textup{There is not enough information to answer the question.}$

$3\sqrt{13}\textup{ feet}$

$40\textup{ feet}$

$3\sqrt{22}\textup{ feet}$

Correct answer:

$5\sqrt{34}\textup{ feet}$

Explanation:

The Pythagorean Theorem states that for any right triangle with legs and and hypotenuse :

a^2 + b^2 = c^2 .

Applying this to Marcus's steps, we know that 15^2 + 25^2 = c^2 .

Expand:

225 + 625 = 850

So, c^2 = 850 . To find , just take the square root:

$\sqrt{850} = \sqrt{25 \cdot 34} = 5\sqrt{34}$

So, Marcus travels exactly $5\sqrt{34}\textup{ feet}$ back to the start.

Report an Error

Example Question #91 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Justin travels $15\textup{ feet}$ to the east and $20\textup{ feet}$ to the north. How far away from his starting point is he now?

Possible Answers:

$30\textup{ ft}$

$25\textup{ ft}$

$45\textup{ ft}$

$35\textup{ ft}$

$22\textup{ ft}$

Correct answer:

$25\textup{ ft}$

Explanation:

This is solving for the hypotenuse of a triangle. Using the Pythagorean Theorem, which says that a^2+b^2=c^2

15^2 + 20^2 = c^2

225+400=c^2

625=c^2

25=c

Report an Error

Example Question #161 : Geometry

Susie walks north from her house to a park that is 30 meters away. Once she arrives at the park, she turns and walks west for 80 meters to a bench to feed some pigeons. She then walks north for another 30 meters to a concession stand. If Susie returns home in a straight line from the concession stand, how far will she walk from the concession stand to her house, in meters?

Possible Answers:

200

100

Correct answer:

100

Explanation:

Susie walks 30 meters north, then 80 meters west, then 30 meters north again. Thus, she walks 60 meters north and 80 meters west. These two directions are 90 degrees away from one another.

At this point, construct a right triangle with one leg that measures 60 meters and a second leg that is 80 meters.

You can save time by using the 3:4:5 common triangle. 60 and 80 are $3\cdot 20$ and $4\cdot 20$ , respectively, making the hypotenuse equal to $5\cdot 20=100$ .

We can solve for the length of the missing hypotenuse by applying the Pythagorean theorem:

$a^{2}+b^{2}=c^{2}$

Substitute the following known values into the formula and solve for the missing hypotenuse: side .

$a= 60,\ b= 80,\ c= ?$

$(60)^{2}+(80)^{2}=c^{2}$

$3600+6400=c^{2}$

$10,000=c^{2}$

c=100

Susie will walk 100 meters to reach her house.

Report an Error

Example Question #441 : Plane Geometry

The lengths of the sides of a triangle are consecutive odd numbers and the triangle's perimeter is 57 centimeters. What is the length, in centimeters, of its longest side?

Possible Answers:

Correct answer:

Explanation:

First, define the sides of the triangle. Because the side lengths are consecutive odd numbers, if we define the shortest side will be as , the next side will be defined as x+2 , and the longest side will be defined as x+4 . We can then find the perimeter of a triangle using the following formula:

$\text{Perimeter}=\text{side}+\text{side}+\text{side}$

Substitute in the known values and variables.

$\text{Perimeter}=x+(x+2)+(x+4)$

57=3x+6

Subtract 6 from both sides of the equation.

57-6=3x+6-6

51=3x

Divide both sides of the equation by 3.

$\frac{51}{3}=\frac{3x}{3}$

Solve.

x=17

This is not the answer; we need to find the length of the longest side, or x+4 .

$\text{Longest side}=x+4$

Substitute in the calculated value for and solve.

$\text{Longest side}=17+4$

$\text{Longest side}=21$

The longest side of the triangle is 21 centimeters long.

Report an Error

Example Question #5 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Each of the following answer choices lists the side lengths of a different triangle. Which of these triangles does not have a right angle?

Possible Answers:

9, 12, 15

$2, 2, 2\sqrt{2}$

5, 12, 13

6,7,12

Correct answer:

6,7,12

Explanation:

6, 7, 12 cannot be the side lengths of a right triangle. 6^2+ 7^2 does not equal 12^2 . Also, special right triangle 3-4-5, 5-12-13, and 45-45-90 rules can eliminate all the other choices.

Report an Error

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

Given a right triangle with a leg length of 6 and a hypotenuse length of 10, find the length of the other leg, x.

Act_math_106

Possible Answers:

Correct answer:

Explanation:

Using Pythagorean Theorem, we can solve for the length of leg x:

x² + 6² = 10²

Now we solve for x:

x² + 36 = 100

x² = 100 – 36

x² = 64

x = 8

Also note that this is proportionally a 3/4/5 right triangle, which is very common. Always look out for a side-to-hypoteneuse ratio of 3/5 or 4/5, or a side-to-side ratio of 3/4, in any right triangle, so that you may solve such triangles rapidly.

Report an Error

Example Question #1 : Right Triangles

In a right triangle a hypotenuse has a length of 8 and leg has a length of 7. What is the length of the third side to the nearest tenth?

Possible Answers:

2.4

1.0

3.6

3.9

Correct answer: 3.9

Explanation:

Using the pythagorean theorem, 8²=7²+x². Solving for x yields the square root of 15, which is 3.9

Report an Error

View ACT Math Tutors

Nafis
Certified Tutor

University of Leipzig, Germany., Bachelor of Science, Physics. University of Pittsburgh-Pittsburgh Campus, Doctor of Philosop...

View ACT Math Tutors

Timothy
Certified Tutor

Bethune-Cookman University, Bachelor of Science, Mathematics. University of Phoenix, Master of Science, Computer and Informat...

View ACT Math Tutors

Troy
Certified Tutor

Rice University, Bachelor in Arts, Kinesiology.

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

SAT Courses & Classes in Chicago, GMAT Courses & Classes in Miami, MCAT Courses & Classes in Houston, Spanish Courses & Classes in Boston, ISEE Courses & Classes in San Diego, GRE Courses & Classes in Houston, Spanish Courses & Classes in New York City, Spanish Courses & Classes in Houston, ACT Courses & Classes in Phoenix, ISEE Courses & Classes in New York City

Popular Test Prep

MCAT Test Prep in Houston, SAT Test Prep in Houston, SSAT Test Prep in Denver, GRE Test Prep in San Diego, ISEE Test Prep in Dallas Fort Worth, ACT Test Prep in Washington DC, GMAT Test Prep in San Diego, GMAT Test Prep in Miami, ACT Test Prep in New York City, MCAT Test Prep in Denver

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 : ACT Math

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #131 : Geometry

Example Question #51 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #52 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #132 : Geometry

Example Question #91 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #161 : Geometry

Example Question #441 : Plane Geometry

Example Question #5 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

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

Example Question #1 : Right Triangles

All ACT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: