We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Precalculus : Law of Cosines and Sines

Study concepts, example questions & explanations for Precalculus

Create An Account

All Precalculus Resources

12 Diagnostic Tests 380 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #31 : Use The Laws Of Cosines And Sines

Find the length of the missing side,

Possible Answers:

5.92

6.91

8.10

6.37

Correct answer:

6.37

Explanation:

First, use the Law of Sines to find the measurement of angle

$\frac{5}{\sin 50}=\frac{3}{\sin C}$

$5\sin C = 2.30$

$\sin C=0.46$

C= 27.39

Recall that all the angles in a triangle need to add up to 180 degrees.

50+27.39+B=180

B=102.61

Now, use the Law of Sines again to find the length of .

$\frac{d}{\sin 102.61}=\frac{5}{\sin 50}$

$d \sin 50= 4.88$

d=6.37

Report an Error

Example Question #71 : Trigonometric Applications

What is the largest possible angle, measured in degrees, in triangle ABC if $\angle A = 30^\circ$ , AB = 10 , and BC = 6 ?

Possible Answers:

$144.56^\circ$

$123.56^\circ$

$93.56^\circ$

$156.56^\circ$

$107.56^\circ$

Correct answer:

$123.56^\circ$

Explanation:

In the ambiguous SSA case, use Law of Sines to solve for the angle opposite the given side.

$\\* \frac {\sin A}{a} = \frac {\sin C}{c} \\* \\* \frac {\sin 30^\circ}{6} = \frac {\sin C}{10} \\* \\* C = \arcsin \left(\frac {10 \sin 30^\circ}{6}\right) \approx 56.44^\circ$

If $C = 56.44^\circ$ , then $B = 93.56^\circ$ .

However! Another possible value of C is $(180 - 56.44)^\circ = 123.56^\circ$ .

In this case the angles will be $30^\circ, 123.56^\circ, 26.44^\circ$ .

This is bigger than $93.56^\circ$ and is consequently the answer.

Report an Error

View Pre-Calculus Tutors

Dejuan
Certified Tutor

University of Illinois at Urbana-Champaign, Bachelor of Science, Electrical Engineering.

View Pre-Calculus Tutors

Leonard
Certified Tutor

Florida State University, Bachelor of Science, Environmental Science.

View Pre-Calculus Tutors

Yucheng
Certified Tutor

The University of Texas at Austin, Bachelor of Science, Mechanical Engineering.

All Precalculus Resources

12 Diagnostic Tests 380 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

ACT Tutors in Miami, ACT Tutors in Atlanta, Algebra Tutors in Dallas Fort Worth, Physics Tutors in Chicago, Reading Tutors in San Francisco-Bay Area, Statistics Tutors in San Francisco-Bay Area, Calculus Tutors in Denver, SSAT Tutors in Houston, Spanish Tutors in Houston, MCAT Tutors in San Diego

Popular Courses & Classes

MCAT Courses & Classes in New York City, Spanish Courses & Classes in New York City, MCAT Courses & Classes in Phoenix, SAT Courses & Classes in Phoenix, SSAT Courses & Classes in Philadelphia, GMAT Courses & Classes in Washington DC, ACT Courses & Classes in San Diego, MCAT Courses & Classes in Washington DC, Spanish Courses & Classes in San Francisco-Bay Area, SSAT Courses & Classes in Miami

Popular Test Prep

ACT Test Prep in Los Angeles, ACT Test Prep in San Francisco-Bay Area, SAT Test Prep in Los Angeles, GMAT Test Prep in Dallas Fort Worth, SAT Test Prep in Miami, GRE Test Prep in New York City, SSAT Test Prep in San Francisco-Bay Area, LSAT Test Prep in Philadelphia, MCAT Test Prep in Houston, LSAT Test Prep in Atlanta

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

Precalculus : Law of Cosines and Sines

Study concepts, example questions & explanations for Precalculus

All Precalculus Resources

Example Questions

Example Question #31 : Use The Laws Of Cosines And Sines

Example Question #71 : Trigonometric Applications

All Precalculus Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: