Precalculus : Solve a Triangle Using the Law of Sines (ASA, SAA, AAS)

Study concepts, example questions & explanations for Precalculus

varsity tutors app store varsity tutors android store

Example Questions

Example Question #1 : Solve A Triangle Using The Law Of Sines (Asa, Saa, Aas)

Use the Law of Sines to find  in the following triangle.

9

(Not drawn to scale.)

Possible Answers:

Correct answer:

Explanation:

We use the Law of Sines to solve this problem

 

we plug in  

 

solving for  we get:

 

Example Question #2 : Solve A Triangle Using The Law Of Sines (Asa, Saa, Aas)

Use the Law of Sines to find .

10 

(Not drawn to scale.)

Possible Answers:

Correct answer:

Explanation:

We use the Law of Sines to solve this problem: 

where 

 

We plug in the values that we will need:

               Notice that we did not use 

 

Solve for  we get:

Example Question #3 : Solve A Triangle Using The Law Of Sines (Asa, Saa, Aas)

Which of the following are the missing sides of the triangle?

11

Possible Answers:

None of the above

Correct answer:

Explanation:

In order to solve this problem, we need to find . We do so by remembering the sum of the angles in a triangle is :

 

We can now use the Law of Sines to find the missing sides.

   

         which is II.

  

   

        which is III.

 

Our answers are then II and III

Example Question #4 : Law Of Sines

Which of the following are the missing sides of the triangle?

 12

Possible Answers:

None of the above

Correct answer:

Explanation:

In order to solve this problem, we need to find  

Since all the angles of a triangle add to , we can easily find it:

We can now use the Law of Sines to find the missing sides:

   

      which is I.

 

   

      which is III.

 

Our answers are then I and III.

Example Question #4 : Solve A Triangle Using The Law Of Sines (Asa, Saa, Aas)

Solve the triangle using the Law of Sines:

Law_of_sines__aas_

Possible Answers:

None of the other answers

Correct answer:

Explanation:

First we need to know what the Law of Sines is:

Looking at the triangle, we know c, C, and B. We can either solve for side b, using the law, or angle A using our knowledge that the interior angles of a triangle must add up to be 180.

Now all that's left is to find side a:

Example Question #5 : Solve A Triangle Using The Law Of Sines (Asa, Saa, Aas)

Use the Law of Sines to solve for the specified variable.

Pcq2

Solve for . Round to the nearest tenth.

Possible Answers:

None of these answers are correct.

Correct answer:

Explanation:

Law of Sines

 

Therefore...

 

After rounding...

Example Question #6 : Solve A Triangle Using The Law Of Sines (Asa, Saa, Aas)

Pcq2

Solve for c using Law of Sines, given:

Round to the nearest tenth.

Possible Answers:

None of these answers are correct.

Correct answer:

Explanation:

Law of Sines

 

Therefore...

After rounding...

Learning Tools by Varsity Tutors

Incompatible Browser

Please upgrade or download one of the following browsers to use Instant Tutoring: