Call Now to Set Up Tutoring:

(888) 888-0446

Trigonometry : Law of Sines

Study concepts, example questions & explanations for Trigonometry

Create An Account

All Trigonometry Resources

6 Diagnostic Tests 155 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Law Of Sines

Given sides a = 10 , b = 5 and angle $\angle A = 100^{\circ}$ determine the corresponding value for $\angle B$

Possible Answers:

$5^{\circ}$

Undefined

$-29.5^{\circ}}$

$29.5^{\circ}$

$60^{\circ}$

Correct answer:

$29.5^{\circ}$

Explanation:

The Law of Sines is used here since we have Side - Angle - Side. We setup our equation as follows:

$\frac{a}{\sin A} = \frac{b}{\sin B}$

Next, we substitute the known values:

$\frac{10}{\sin 100} = \frac{5}{\sin B}$

Now we cross multiply:

$10\sin B = 5\sin 100$

Divide by 10 on both sides:

$\sin B = 0.5\sin100$

Finally taking the inverse sine to obtain the desired angle:

$B = sin^{-1}\left(0.5\sin100\right ) = 29.5^{\circ}$

Report an Error

Example Question #1 : Law Of Sines

Let $\angle A = 17^{\circ}$ , $\angle C = 110^{\circ}$ and a = 5 , determine the length of side .

Possible Answers:

16.07

5.88

1.83

5.21

13.66

Correct answer:

13.66

Explanation:

We have two angles and one side, however we do not have $\angle B$ . We can determine the angle using the property of angles in a triangle summing to $180^{\circ}$ :

$\angle B = 180^{\circ} - 17^{\circ} - 110^{\circ} = 53^{\circ}$

Now we can simply utilize the Law of Sines:

$\frac{5}{\sin 17} = \frac{b}{\sin 53}$

Cross multiply and divide:

$\frac{5\sin 53}{\sin 17} = b$

Reducing to obtain the final solution:

b = 13.66

Report an Error

Example Question #2 : Law Of Sines

Triangle

In the above triangle, $a = 35^{\circ}$ and $c = 93^{\circ}$ . If X = 49 , what is to the nearest tenth? (note: triangle not to scale)

Possible Answers:

62.1

35.7

28.1

67.3

38.7

Correct answer:

38.7

Explanation:

If we solve for , we can use the Law of Sines to find .

Since the sum of angles in a triangle equals $180^{\circ}$ ,

$a + b + c = 180^{\circ}$

$35^{\circ} + b + 93^{\circ} = 180^{\circ}$

$b = 52^{\circ}$

Now, using the Law of Sines:

$\frac{\textup{side opposite a}}{\sin\left ( a\right )} = \frac{\textup{side opposite b}}{\sin\left ( b\right )} = \frac{\textup{side opposite c}}{\sin\left ( c\right )}$

$\frac{{X}}{\sin\left ( c\right )} = \frac{{Y}}{\sin\left ( b\right )}$

$\frac{{49}}{\sin\left ( 93^{\circ}\right )} = \frac{{Y}}{\sin\left ( 52^{\circ}\right )}$

$\frac{49}{0.999} \approx \frac{Y}{0.788}$

$Y \approx \frac{49 \cdot 0.788 }{0.999}$

$Y \approx 38.7$

Report an Error

Example Question #2 : Law Of Sines

Screen_shot_2015-03-07_at_5.09.32_pm

By what factor is larger than in the triangle pictured above.

Possible Answers:

0.66

1.8

It isn't

1.51

Correct answer:

1.51

Explanation:

The Law of Sines states

$\frac{a}{\sin(A)}=\frac{b}{\sin(B)}=\frac{c}{\sin(C)}$

so for a and b, that sets up

$\frac{a}{\sin(35)}=\frac{b}{\sin(60)}, b=a\frac{\sin(60)}{\sin(35)}=1.51a$

Report an Error

Example Question #1 : Law Of Sines

Solve for $\theta$ :
Sines 1

Possible Answers:

0.15^o

7.24 ^ o

45.49^o

68.18 ^o

47.5 ^ o

Correct answer:

68.18 ^o

Explanation:

To solve, use the law of sines, $\frac{ \sin A }{a } = \frac{ \sin B }{b}$ where a is the side across from the angle A, and b is the side across from the angle B.

$\frac{ \sin \theta }{ 19 } = \frac{ \sin ( 20^o )}{ 7 }$ cross-multiply

$7 \sin \theta = 19 \cdot \sin (20^o )$ evaluate the right side

$7 \sin \theta = 6.4984$ divide by 7

$\sin \theta = 0.9283$ take the inverse sine

$\theta = \sin ^ {-1 } (0.9283 ) \approx 68.18 ^o$

Report an Error

Example Question #1 : Law Of Sines

Evaluate using law of sines:

Sines 2

Possible Answers:

2.96

7.72

6.34

16.56

3.26

Correct answer:

7.72

Explanation:

To solve, use law of sines, $\frac{ \sin A }{a} = \frac{ \sin B }{b}$ where side a is across from angle A, and side b is across from angle B.

In this case, we have a 90-degree angle across from x, but we don't currently know the angle across from the side length 7. We can figure out this angle by subtracting 25^o from 90^o :

90^o - 25 ^o = 65^o

Now we can set up and solve using law of sines:

$\frac{ \sin (65^o )}{ 7 } = \frac{ \sin (90 ^o )} { x }$ cross-multiply

$\sin (90 ^o ) \cdot 7 = \sin (65^o ) \cdot x$ evaluate the sines

$1 \cdot 7 = (0.9063) x$ divide by 0.9063

7.72 = x

Report an Error

Example Question #1 : Law Of Sines

What is the measure of $\angle F$ in $\triangle DEF$ below? Round to the nearest tenth of a degree.

Triangle def

Possible Answers:

$18.2^\circ$

$47.8^\circ$

$20.0^\circ$

$16.6^\circ$

$0.3^\circ$

Correct answer:

$16.6^\circ$

Explanation:

The law of sines tells us that $\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}$ , where a, b, and c are the sides opposite of angles A, B, and C. In $\triangle DEF$ , these ratios can be used to find $\angle F$ :

$\frac{sinD}{d}=\frac{sinF}{f}$

$\frac{sin114^\circ}{16}=\frac{sin F}{5}$

$sinF=\frac{5sin114^\circ}{16}$

$F=sin^{-1}\left ( \frac{5sin114^\circ}{16}\right )$

$F\approx16.6^\circ$

Report an Error

Example Question #1 : Law Of Sines

Find the length of the line segment $\overline{AB}$ in the triangle below.

Round to the nearest hundredth of a centimeter.

Triangle

Possible Answers:

$10.83\ cm$

$14.66\ cm$

$15.60\ cm$

$12.21\ cm$

$13.84\ cm$

Correct answer:

$13.84\ cm$

Explanation:

The law of sines states that

$\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}$ .

In this triangle, we are looking for the side length c, and we are given angle A, angle B, and side b. The sum of the interior angles of a triangle is $180^{\circ}$ ; using subtraction we find that angle C = $57^{\circ}$ .

We can now form a proportion that includes only one unknown, c:

$\frac{sin52^{\circ}}{13}=\frac{sin57^{\circ}}{c}$

Solving for c, we find that

$c=\frac{13sin57^{\circ}}{sin52^{\circ}}\approx13.84$ .

Report an Error

Example Question #1 : Law Of Sines

In the triangle below, $m\angle A=78^\circ$ , $m\angle B=40^\circ$ , and c=14 . What is the length of side to the nearest tenth?

Triangle abc

Possible Answers:

10.2

12.6

15.5

9.2

19.2

Correct answer:

10.2

Explanation:

First, find $m\angle C$ . The sum of the interior angles of a triangle is $180^\circ$ , so $m\angle C = 180^\circ - 78^\circ - 40^\circ$ , or $62^\circ$ .

Using this information, you can set up a proportion to find side b:

$\frac{sinC}{c}=\frac{sinB}{b}$

$\frac{sin62^\circ}{14}=\frac{sin40^\circ}{b}$

$b=\frac{14sin40^\circ}{sin62^\circ}$

$b\approx10.2$

Report an Error

Example Question #1 : Law Of Sines

In the triangle below, $m\angle A=75^\circ$ , $m\angle B=21^\circ$ , and c=19.3 .

Triangle abc

What is the length of side a to the nearest tenth?

Possible Answers:

7.0

7.2

19.9

52.0

18.7

Correct answer:

18.7

Explanation:

To use the law of sines, first you must find the measure of $\angle C$ . Since the sum of the interior angles of a triangle is $180^\circ$ , $m\angle C=84^\circ$ .

Law of sines:

$\frac{\sin A}{a}=\frac{\sin C}{c}$

$\frac{\sin 75^\circ}{a}=\frac{\sin 84^\circ}{19.3}$

$a=\frac{19.3 \sin 75^\circ}{\sin 84^\circ}$

$a\approx 18.7$

Report an Error

View Trigonometry Tutors

Abhisek
Certified Tutor

University of Florida, Bachelor of Engineering, Computer Science.

View Trigonometry Tutors

Andrew
Certified Tutor

University of Wisconsin-Stevens Point, Bachelor of Science, Mathematics. University of Wisconsin-Oshkosh, Master of Science, ...

View Trigonometry Tutors

Michael
Certified Tutor

Cleveland State University, Bachelor of Science, Mathematics.

All Trigonometry Resources

6 Diagnostic Tests 155 Practice Tests Question of the Day Flashcards Learn by Concept

Trigonometry Tutors in Top Cities:

Popular Courses & Classes

ISEE Courses & Classes in Dallas Fort Worth, MCAT Courses & Classes in Seattle, GRE Courses & Classes in Denver, GMAT Courses & Classes in Phoenix, MCAT Courses & Classes in Denver, SAT Courses & Classes in Chicago, MCAT Courses & Classes in Boston, SSAT Courses & Classes in New York City, SAT Courses & Classes in Washington DC, ISEE Courses & Classes in San Diego

Popular Test Prep

SAT Test Prep in Phoenix, ISEE Test Prep in Denver, LSAT Test Prep in New York City, GMAT Test Prep in Chicago, SSAT Test Prep in Atlanta, GMAT Test Prep in Miami, MCAT Test Prep in San Francisco-Bay Area, SSAT Test Prep in San Francisco-Bay Area, GRE Test Prep in Seattle, ACT Test Prep in San Francisco-Bay Area

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

Trigonometry : Law of Sines

Study concepts, example questions & explanations for Trigonometry

All Trigonometry Resources

Example Questions

Example Question #1 : Law Of Sines

Example Question #1 : Law Of Sines

Example Question #2 : Law Of Sines

Example Question #2 : Law Of Sines

Example Question #1 : Law Of Sines

Example Question #1 : Law Of Sines

Example Question #1 : Law Of Sines

Example Question #1 : Law Of Sines

Example Question #1 : Law Of Sines

Example Question #1 : Law Of Sines

All Trigonometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: