We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Trigonometry : Triangles

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 #11 : Law Of Cosines And Law Of Sines

In degrees, find the value of angle B.

Possible Answers:

17.04

18.94

15.44

16.21

Correct answer:

16.21

Explanation:

In order to find the value of the angle, you will need to use the law of cosines. Recall that for any triangle, like the one shown below,

$\cos A=\frac{b^2+c^2-a^2}{2bc}$

$\cos B=\frac{a^2+c^2-b^2}{2ac}$

$\cos C=\frac{a^2+b^2-c^2}{2ab}$

Now, since we want to find the value of B, we will need to use $\cos B=\frac{a^2+c^2-b^2}{2ac}$ .

Plug in the given values of the triangle.

$\cos B=\frac{11^2+8^2-4^2}{2(11)(8)}=0.960$

B=16.21 degrees

Make sure to round to places after the decimal.

Report an Error

Example Question #12 : Law Of Cosines And Law Of Sines

In degrees, find the value of angle B.

Possible Answers:

32.48

28.96

30.40

29.51

Correct answer:

28.96

Explanation:

In order to find the value of the angle, you will need to use the law of cosines. Recall that for any triangle, like the one shown below,

$\cos A=\frac{b^2+c^2-a^2}{2bc}$

$\cos B=\frac{a^2+c^2-b^2}{2ac}$

$\cos C=\frac{a^2+b^2-c^2}{2ab}$

Now, since we want to find the value of B, we will need to use $\cos B=\frac{a^2+c^2-b^2}{2ac}$ .

Plug in the given values of the triangle.

$\cos B=\frac{12^2+9^2-6^2}{2(12)(9)}=0.875$

B=28.96 degrees

Make sure to round to places after the decimal.

Report an Error

Example Question #13 : Law Of Cosines And Law Of Sines

In degrees, find the value of angle C.

Possible Answers:

52.01

41.22

49.46

44.78

Correct answer:

49.46

Explanation:

In order to find the value of the angle, you will need to use the law of cosines. Recall that for any triangle, like the one shown below,

$\cos A=\frac{b^2+c^2-a^2}{2bc}$

$\cos B=\frac{a^2+c^2-b^2}{2ac}$

$\cos C=\frac{a^2+b^2-c^2}{2ab}$

Now, since we want to find the value of C, we will need to use $\cos C=\frac{a^2+b^2-c^2}{2ab}$ .

Plug in the given values of the triangle.

$\cos C=\frac{15^2+6^2-12^2}{2(15)(6)}=0.65$

C=49.46 degrees

Make sure to round to places after the decimal.

Report an Error

Example Question #301 : Trigonometry

In degrees, find the value of angle C.

Possible Answers:

42.59

40.08

39.51

41.80

Correct answer:

41.80

Explanation:

In order to find the value of the angle, you will need to use the law of cosines. Recall that for any triangle, like the one shown below,

$\cos A=\frac{b^2+c^2-a^2}{2bc}$

$\cos B=\frac{a^2+c^2-b^2}{2ac}$

$\cos C=\frac{a^2+b^2-c^2}{2ab}$

Now, since we want to find the value of C, we will need to use $\cos C=\frac{a^2+b^2-c^2}{2ab}$ .

Plug in the given values of the triangle.

$\cos C=\frac{5^2+11^2-8^2}{2(5)(11)}=0.74545$

C=41.80 degrees

Make sure to round to places after the decimal.

Report an Error

Example Question #15 : Law Of Cosines And Law Of Sines

Find the length of side .

Possible Answers:

20.92

17.85

19.01

18.44

Correct answer:

17.85

Explanation:

In order to find the value of the angle, you will need to use the law of cosines. Recall that for any triangle, like the one shown below,

$a^2=b^2+c^2-2bc\cos A$

Plug in the given values of the triangle.

$a^2=12^2+13^2-2(12)(13)\cos 91$

a=17.85

Make sure to round to places after the decimal.

Report an Error

Example Question #52 : Triangles

In degrees, find the value of angle A.

Possible Answers:

66.24

59.63

71.05

67.23

Correct answer:

67.23

Explanation:

In order to find the value of the angle, you will need to use the law of cosines. Recall that for any triangle, like the one shown below,

$\cos A=\frac{b^2+c^2-a^2}{2bc}$

$\cos B=\frac{a^2+c^2-b^2}{2ac}$

$\cos C=\frac{a^2+b^2-c^2}{2ab}$

Now, since we want to find the value of A, we will need to use $\cos A=\frac{b^2+c^2-a^2}{2bc}$ .

Plug in the given values of the triangle.

$\cos A=\frac{17^2+19^2-20^2}{2(17)(19)}=0.387$

A=67.23 degrees

Make sure to round to places after the decimal.

Report an Error

Example Question #11 : Law Of Cosines And Law Of Sines

In degrees, find the value of angle A.

Possible Answers:

Correct answer:

Explanation:

In order to find the value of the angle, you will need to use the law of cosines. Recall that for any triangle, like the one shown below,

$\cos A=\frac{b^2+c^2-a^2}{2bc}$

$\cos B=\frac{a^2+c^2-b^2}{2ac}$

$\cos C=\frac{a^2+b^2-c^2}{2ab}$

Now, since we want to find the value of A, we will need to use $\cos A=\frac{b^2+c^2-a^2}{2bc}$ .

Plug in the given values of the triangle.

$\cos A=\frac{15^2+20^2-25^2}{2(15)(20)}=0$

A=90 degrees

Report an Error

Example Question #21 : Law Of Cosines

In degrees, find the value of angle A.

Possible Answers:

108.21

102.56

115.61

109.04

Correct answer:

108.21

Explanation:

In order to find the value of the angle, you will need to use the law of cosines. Recall that for any triangle, like the one shown below,

$\cos A=\frac{b^2+c^2-a^2}{2bc}$

$\cos B=\frac{a^2+c^2-b^2}{2ac}$

$\cos C=\frac{a^2+b^2-c^2}{2ab}$

Now, since we want to find the value of A, we will need to use $\cos A=\frac{b^2+c^2-a^2}{2bc}$ .

Plug in the given values of the triangle.

$\cos A=\frac{2^2+4^2-5^2}{2(2)(4)}=-0.3125$

A=108.21 degrees

Make sure to round to places after the decimal.

Report an Error

Example Question #21 : Law Of Cosines

In triangle $\triangle ABC$ , $\measuredangle A = 115^{\circ}$ , AB = 31 and AC = 42 . To the nearest tenth, what is {}BC ?

Possible Answers:

61.9

71.3

40.3

3825.5

57.3

Correct answer:

61.9

Explanation:

By the Law of Cosines,

$BC^2 = AB^2 +AC^2 - 2\left (AB\right )\left ( AC\right )\cos\angle A$

or, equivalently,

$BC = \sqrt[]{AB^2 +AC^2 - 2\left ( AB\right )\left ( AC\right )\cos \angle A}$

Substitute:

$BC = \sqrt[]{31^2 + 42^2 - 2\left ( 31\right )\left ( 42\right )\cos \left ( 115^{\circ}\right )}$

$\textup{BC}= \sqrt[]{961 + 1764 - 2604\cdot (-0.4226)} \approx \sqrt{2725 + 1100} \approx \sqrt{3825}\approx61.9$

Report an Error

Example Question #51 : Triangles

Solve for $\theta$ :

Cosines 2

Possible Answers:

83.04 ^o

14.36^o

41.41 ^o

124.23^o

88.57^o

Correct answer:

41.41 ^o

Explanation:

Solve using law of cosines: $c^2 = a^2 + b^2 - 2ab \cdot \cos C$ where C is the angle between sides a and b.

$8^2 = 3^2 + 10^2 - 2(3)(10) \cos \theta$

$64 = 109 - 60 \cos \theta$ subtract 109 from both sides

$- 45 = -60 \cos \theta$ divide by -60

$0.75 = \cos \theta$ take the inverse cosine using a calculator

$41.41 = \theta$

Sometimes with law of cosines we have to worry about a second angle that the calculator won't give us. In this case, that would be 360 - 41.41=318.59 but that is too big an angle to be in a triangle.

Report an Error

View Trigonometry Tutors

Dalton
Certified Tutor

University of Massachusetts Amherst, Doctor of Philosophy, Mathematics.

View Trigonometry Tutors

Vandana
Certified Tutor

Jawaharlal Nehru Technological University, Bachelor of Technology, Civil Engineering. Florida International University, Maste...

View Trigonometry Tutors

Vicky
Certified Tutor

Clemson University, Doctor of Science, Civil Engineering.

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

MCAT Courses & Classes in San Francisco-Bay Area, MCAT Courses & Classes in San Diego, SAT Courses & Classes in Boston, GMAT Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in Houston, GMAT Courses & Classes in Seattle, GRE Courses & Classes in San Diego, LSAT Courses & Classes in Houston, SSAT Courses & Classes in San Diego, Spanish Courses & Classes in San Francisco-Bay Area

Popular Test Prep

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

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 : Triangles

Study concepts, example questions & explanations for Trigonometry

All Trigonometry Resources

Example Questions

Example Question #11 : Law Of Cosines And Law Of Sines

Example Question #12 : Law Of Cosines And Law Of Sines

Example Question #13 : Law Of Cosines And Law Of Sines

Example Question #301 : Trigonometry

Example Question #15 : Law Of Cosines And Law Of Sines

Example Question #52 : Triangles

Example Question #11 : Law Of Cosines And Law Of Sines

Example Question #21 : Law Of Cosines

Example Question #21 : Law Of Cosines

Example Question #51 : Triangles

All Trigonometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: