We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Precalculus : The Ambiguous Case (SSA, ASS)

Study concepts, example questions & explanations for Precalculus

CREATE AN ACCOUNT Create Tests & Flashcards

Home Embed

All Precalculus Resources

12 Diagnostic Tests 400 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

← Previous 1 2 Next →

Example Question #1 : The Ambiguous Case (Ssa, Ass)

Triangle_700

Given b=4ft, c=6ft, and $B=36^\circ$ , what is the measurement of to the nearest degree?

Possible Answers:

$83^\circ$

$82.15^\circ$

$82.2^\circ$

$82^\circ$

Correct answer:

$82^\circ$

Explanation:

Using the information we have, we can solve for $\angle C$ :

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

Plugging in what we know, we have:

$\frac{sin(36)}{4}=\frac{sinC}{6}$ .

Then, solve for sinC :

$6\cdot\frac{sin(36)}{4}=sinC$ .

Simplify, then solve for : 0.8816778784=sinC which means $sin^{-1}(.8816778784)=C$ .

Therefore, after rounding to the nearest degree, $C=62^\circ$ .

To solve for $\angle A$ , subtract $\angle B$ and $\angle C$ from $180^\circ$ : $180^\circ-36^\circ-62^\circ=82^\circ$ .

Therefore, $\angle A = 82^\circ$ .

Report an Error

Example Question #2 : The Ambiguous Case (Ssa, Ass)

Find the length of the missing side, .

Possible Answers:

26.77

22.36

24.51

29.01

Correct answer:

22.36

Explanation:

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

$\frac{15}{\sin 41}=\frac{20}{\sin B}$

$15\sin B = 13.12$

$\sin B=0.87$

B= 61.01

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

41+61.01+A=180

A=77.99

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

$\frac{d}{\sin 77.99}=\frac{15}{\sin 41}$

$d \sin 41= 14.67$

d=22.36

Report an Error

Example Question #3 : The Ambiguous Case (Ssa, Ass)

Find the length of the missing side, .

Possible Answers:

29.12

28.54

20.57

25.53

Correct answer:

25.53

Explanation:

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

$\frac{12}{\sin 21}=\frac{16}{\sin B}$

$12\sin B = 5.73$

$\sin B=0.48$

B= 28.69

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

21+28.69+A=180

A=130.31

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

$\frac{d}{\sin 130.31}=\frac{12}{\sin 21}$

$d \sin 21= 9.15$

d=25.53

Report an Error

Example Question #1 : The Ambiguous Case (Ssa, Ass)

Find the length of the missing side, .

Possible Answers:

9.89

12.44

10.73

8.14

Correct answer:

10.73

Explanation:

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

$\frac{6}{\sin34}=\frac{9}{\sin B}$

$6 \sin B = 5.03$

$\sin B=0.84$

B= 57.14

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

34+57.14+A=180

A=88.86

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

$\frac{d}{\sin 88.86}=\frac{6}{\sin 34}$

$d \sin 34=5.9988$

d=10.73

Report an Error

Example Question #1 : The Ambiguous Case (Ssa, Ass)

Find the length of the missing side,

Possible Answers:

15.12

14.63

13.98

12.37

Correct answer:

14.63

Explanation:

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

$\frac{13}{\sin 54}=\frac{14}{\sin B}$

$13\sin B = 11.33$

$\sin B=0.87$

B= 60.46

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

54+60.46+C=180

C=65.54

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

$\frac{d}{\sin 65.54}=\frac{13}{\sin 54}$

$d \sin 54= 11.83$

d=14.63

Report an Error

Example Question #2 : The Ambiguous Case (Ssa, Ass)

Find the length of the missing side,

Possible Answers:

7.84

9.51

8.81

8.95

Correct answer:

8.95

Explanation:

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

$\frac{6}{\sin 41}=\frac{8}{\sin B}$

$6\sin B = 5.25$

$\sin B=0.875$

B= 61.04

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

41+61.04+C=180

C=77.96

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

$\frac{d}{\sin 77.96}=\frac{6}{\sin 41}$

$d \sin 41= 5.87$

d=8.95

Report an Error

Example Question #1 : The Ambiguous Case (Ssa, Ass)

Find the length of the missing side, .

Possible Answers:

11.71

15.62

19.35

14.12

Correct answer:

15.62

Explanation:

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

$\frac{9}{\sin 35}=\frac{12}{\sin B}$

$9\sin B = 6.88$

$\sin B=0.76$

B= 49.46

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

35+49.46+C=180

C=95.54

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

$\frac{d}{\sin 95.54}=\frac{9}{\sin 35}$

$d \sin 35= 8.96$

d=15.62

Report an Error

Example Question #1 : The Ambiguous Case (Ssa, Ass)

Find the length of the missing side, .

Possible Answers:

20.18

28.91

27.98

24.71

Correct answer:

27.98

Explanation:

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

$\frac{17}{\sin 33}=\frac{16}{\sin C}$

$17\sin C = 8.71$

$\sin C= 0.51$

C= 30.66

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

33+30.66+B=180

B=116.34

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

$\frac{d}{\sin 116.34}=\frac{17}{\sin 33}$

$d \sin 33= 15.24$

d=27.98

Report an Error

Example Question #1 : The Ambiguous Case (Ssa, Ass)

Find the length of the missing side,

Possible Answers:

24.12

35.91

31.50

29.07

Correct answer:

31.50

Explanation:

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

$\frac{19}{\sin 37}=\frac{24}{\sin C}$

$19\sin C = 14.44$

$\sin C= 0.76$

C= 49.46

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

37+49.46+B=180

B=93.54

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

$\frac{d}{\sin 93.54}=\frac{19}{\sin 37}$

$d \sin 37 = 18.96$

d=31.50

Report an Error

Example Question #411 : Pre Calculus

Find the length of the missing side, .

Possible Answers:

9.28

9.92

7.64

10.25

Correct answer:

10.25

Explanation:

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

$\frac{7}{\sin 29}=\frac{4}{\sin C}$

$7\sin C = 1.94$

$\sin C= 0.28$

C= 16.26

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

16.26+29+B=180

B=134.74

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

$\frac{d}{\sin 134.74}=\frac{7}{\sin 29}$

$d \sin 29= 4.97$

d=10.25

Report an Error

← Previous 1 2 Next →

View Pre-Calculus Tutors

Anastasia
Certified Tutor

Moscow University, Bachelor of Science, Theoretical and Mathematical Physics. Princeton University, Doctor of Science, Theore...

View Pre-Calculus Tutors

Michael
Certified Tutor

Christopher Newport University, Bachelor in Arts, Mathematics.

View Pre-Calculus Tutors

Sharif
Certified Tutor

University of South Florida-Main Campus, Bachelor of Science, Cellular and Molecular Biology.

All Precalculus Resources

12 Diagnostic Tests 400 Practice Tests Question of the Day Flashcards Learn by Concept

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 : The Ambiguous Case (SSA, ASS)

Study concepts, example questions & explanations for Precalculus

All Precalculus Resources

Example Questions

Example Question #1 : The Ambiguous Case (Ssa, Ass)

Example Question #2 : The Ambiguous Case (Ssa, Ass)

Example Question #3 : The Ambiguous Case (Ssa, Ass)

Example Question #1 : The Ambiguous Case (Ssa, Ass)

Example Question #1 : The Ambiguous Case (Ssa, Ass)

Example Question #2 : The Ambiguous Case (Ssa, Ass)

Example Question #1 : The Ambiguous Case (Ssa, Ass)

Example Question #1 : The Ambiguous Case (Ssa, Ass)

Example Question #1 : The Ambiguous Case (Ssa, Ass)

Example Question #411 : Pre Calculus

All Precalculus Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

FIND THE BEST TUTORS

Email address:
Your name:

Email address:
Your name:
Feedback: