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 #1 : How To Find A Missing Side With Sine

Circle_chord_2

The above circle has a radius of and a center at . $\angle A = 127^{\circ}$ . Find the length of chord $\overline{BC}$ .

Possible Answers:

11.3

14.3

7.1

12.8

Correct answer:

14.3

Explanation:

We can solve for the length of the chord by drawing a line the bisects the angle and the chord, shown below as $\overline{AD}$ .

Circle_chord_4

In this circle, we can see the triangle $\bigtriangleup ADC$ has a hypotenuse equal to the radius of the circle ( $\overline{AC}$ ), an angle $\theta$ equal to half the angle made by the chord, and a side $\overline{CD}$ that is half the length of the chord. By using the sine function, we can solve for $\overline{CD}$ .

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

$\sin \left (\theta\right ) = \frac{\overline{CD}}{\overline{AC}}$

$\sin \left ( 63.5^{\circ}\right ) = \frac{\overline{CD}}{8}$

$8\sin \left ( 63.5^{\circ}\right ) = \overline{CD}$

$7.16 = \overline{CD}$

The length of the entire chord is twice the length of $\overline{CD}$ , so the entire chord length is 14.3 .

Report an Error

Example Question #4 : How To Find A Missing Side With Sine

Sin47

What is in the right triangle above? Round to the nearest hundredth.

Possible Answers:

$\small 21.78$

$\small 41.93$

$\small 24.54$

$\small 38.52$

$\small 31.31$

Correct answer:

$\small 21.78$

Explanation:

Recall that the sine of an angle is the ratio of the opposite side to the hypotenuse of that triangle. Thus, for this triangle, we can say:

$\small sin(27.45)=\frac{x}{47.25}$

Solving for $\small x$ , we get:

$\small 47.25*sin(27.45)=x$

$\small x=21.7810391968006$ or $\small 21.78$

Report an Error

Example Question #2 : How To Find A Missing Side With Sine

A man has set up a ground-level sensor to look from the ground to the top of a $30\textup{ foot}$ tall building. The sensor must have an angle of $25 . 5$^{\circ}$$ upward to the top of the building. How far is the sensor from the top of the building? Round to the nearest inch.

Possible Answers:

$69\textup{ feet and 8 inches}$

$33\textup{ feet and 9 inches}$

$10\textup{ feet and }9\textup{ inches}$

$62\textup{ feet and 11 inches}$

$69\textup{ feet and 4 inches}$

Correct answer:

$69\textup{ feet and 8 inches}$

Explanation:

Begin by drawing out this scenario using a little right triangle:

Sin30

Note importantly: We are looking for $\small x$ as the the distance to the top of the building. We know that the sine of an angle is equal to the ratio of the side opposite to that angle to the hypotenuse of the triangle. Thus, for our triangle, we know:

$\small sin(25.5) =\frac{30}{x}$

Using your calculator, solve for :

$\small \small x=\frac{30}{sin(25.5)}$

This is $\small 69.6846149202954$ . Now, take the decimal portion in order to find the number of inches involved.

$\small 0.6846149202954 * 12 = 8.2153790435448$

Thus, rounded, your answer is $\small 69$ feet and $\small 8$ inches.

Report an Error

Example Question #1 : How To Find A Missing Side With Sine

Below is right triangle ABC with sides $a, \: b, \:c$ . What is $\sin(A)$ ?

Right triangle

Possible Answers:

$\frac{a}{b}$

$\frac{c}{a}$

$\frac{b}{c}$

$\frac{a}{c}$

$\frac{b}{a}$

Correct answer:

$\frac{a}{c}$

Explanation:

Right triangle

To find the sine of an angle, remember the mnemonic SOH-CAH-TOA.
This means that

$\textup{sin} = \frac{\textup{opposite}}{\textup{hypotenuse}}$
$\cos = \frac{\textup{adjacent}}{\textup{hypotenuse}}$

$\tan = \frac{\textup{opposite}}{\textup{adjacent}}$ .

We are asked to find the $\sin(A)$ . So at point we see that side is opposite, and the hypotenuse never changes, so it is always . Thus we see that
$\sin(A) = \frac{a}{c}$

Report an Error

Example Question #26 : Sine

In a given right triangle $\Delta ABC$ , hypotenuse AC = 25 and $\angle A = 42^{\circ}$ . Using the definition of $\sin$ , find the length of leg . Round all calculations to the nearest tenth.

Possible Answers:

22.5

11.5

8.5

2.0

17.5

Correct answer:

17.5

Explanation:

In right triangles, SOHCAHTOA tells us that $\sin A = \frac{\textup{opposite}}{\textup{hypotenuse}}$ , and we know that $\angle A = 42^{\circ}$ and hypotenuse AC = 25 . Therefore, a simple substitution and some algebra gives us our answer.

$\sin 42^{\circ} = \frac{CB}{25}$

$.7 = \frac{CB}{25}$ Use a calculator or reference to approximate cosine.

17.5= CB Isolate the variable term.

Thus, 17.5= CB .

Report an Error

Example Question #5 : How To Find A Missing Side With Sine

In a given right triangle $\Delta ABC$ , hypotenuse AC = 5400 and $\angle A = 33^{\circ}$ . Using the definition of $\sin$ , find the length of leg . Round all calculations to the nearest tenth.

Possible Answers:

2916

2798

3110

2845

3313

Correct answer:

2916

Explanation:

In right triangles, SOHCAHTOA tells us that $\sin A = \frac{\textup{opposite}}{\textup{hypotenuse}}$ , and we know that $\angle A = 33^{\circ}$ and hypotenuse AC = 5400 . Therefore, a simple substitution and some algebra gives us our answer.

$\sin 33^{\circ} = \frac{CB}{5400}$

$.54 = \frac{CB}{5400}$ Use a calculator or reference to approximate cosine.

2916= CB Isolate the variable term.

Thus, 2916= CB .

Report an Error

Example Question #81 : Trigonometry

In a given right triangle $\Delta ABC$ , hypotenuse AC = 17 and $\angle A = 45^{\circ}$ . Using the definition of $\sin$ , find the length of leg . Round all calculations to the nearest hundredth.

Possible Answers:

12.02

14.40

12.04

18.52

23.03

Correct answer:

12.02

Explanation:

In right triangles, SOHCAHTOA tells us that $\sin A = \frac{\textup{opposite}}{\textup{hypotenuse}}$ , and we know that $\angle A = 45^{\circ}$ and hypotenuse AC = 17 . Therefore, a simple substitution and some algebra gives us our answer.

$\sin 45^{\circ} = \frac{CB}{17}$

$17\cdot \sin 45^{\circ}= CB$ Isolate the variable term.

Thus, 12.02= CB .

Report an Error

Example Question #1 : How To Find The Sine Of An Angle

Varisty_tutor_images_1

What is the sine of $\angle ACB$ ?

Possible Answers:

$\frac{12}{13}$

$60^{\circ}$

$\frac{12}{5}$

$\frac{5}{12}$

$\frac{5}{13}$

Correct answer:

$\frac{5}{13}$

Explanation:

Sine can be found using the SOH CAH TOA method. For sine we do $\frac{opposite}{hypotenuse}$ .

Report an Error

Example Question #2 : How To Find The Sine Of An Angle

Triangle

See right triangle ABC. If the length AB is 8 and the length of BC is 6, what is the sine of angle A?

Possible Answers:

0.6

0.8

Correct answer:

0.6

Explanation:

Sine A = Opposite / Hypotenuse = BC / AC

To find AC, use Pythagorean Theorum

AB² + BC² = AC²

8² + 6² = AC²

64 + 36 = AC²

100 = AC²

AC = 10

Sine A = BC / AC = 6 / 10 = 0.6

Report an Error

Example Question #3 : How To Find The Sine Of An Angle

Solve for $\sin^2{Q}+3\sin{Q}=-2$ over the interval $0\leq Q \leq 2\pi$

Possible Answers:

Q = 3π or does not exist 2

Q = π or does not exist 2

Q = π or 3π 2 2

Q = π or 2π

Correct answer:

Q = 3π or does not exist 2

Explanation:

Substitute x = sinQ and solve the new equation x² + 3x = –2 by factoring. Be sure to change variables back to Q. As a result, sinQ = –1 or sinQ = –2. This function is bounded between –1 and 1 so sinQ can never be –2 and sinQ is –1 only at 3π/2 or 270 °.

Report an Error

View ACT Math Tutors

Jethro
Certified Tutor

Federal University of Agriculture Abeokuta,, Bachelor of Engineering, Mechatronics, Robotics, and Automation Engineering.

View ACT Math Tutors

Colton
Certified Tutor

Texas State University-San Marcos, Bachelor of Science, Mathematics.

View ACT Math Tutors

Jonathan
Certified Tutor

University of Illinois at Chicago, Bachelor in Arts, Criminal Justice. Syracuse University, Masters in Business Administratio...

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

LSAT Courses & Classes in Atlanta, ACT Courses & Classes in Seattle, SSAT Courses & Classes in Denver, GMAT Courses & Classes in Miami, SAT Courses & Classes in Washington DC, ACT Courses & Classes in Chicago, GRE Courses & Classes in Chicago, MCAT Courses & Classes in Houston, MCAT Courses & Classes in Denver, MCAT Courses & Classes in Miami

Popular Test Prep

GRE Test Prep in Denver, SAT Test Prep in Dallas Fort Worth, LSAT Test Prep in Miami, GMAT Test Prep in Atlanta, LSAT Test Prep in San Diego, MCAT Test Prep in Phoenix, GMAT Test Prep in San Francisco-Bay Area, ACT Test Prep in San Francisco-Bay Area, SAT Test Prep in Philadelphia, SSAT 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 #1 : How To Find A Missing Side With Sine

Example Question #4 : How To Find A Missing Side With Sine

Example Question #2 : How To Find A Missing Side With Sine

Example Question #1 : How To Find A Missing Side With Sine

Example Question #26 : Sine

Example Question #5 : How To Find A Missing Side With Sine

Example Question #81 : Trigonometry

Example Question #1 : How To Find The Sine Of An Angle

Example Question #2 : How To Find The Sine Of An Angle

Example Question #3 : How To Find The Sine Of An Angle

All ACT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: