Precalculus : Use the laws of cosines and sines

Study concepts, example questions & explanations for Precalculus

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Example Questions

Example Question #11 : Law Of Cosines And Sines

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

Pcq1

Solve for . Round to the nearest tenth.

Possible Answers:

None of these answers are correct.

Correct answer:

Explanation:

Law of Cosines

Therefore...

After rounding...

Example Question #1441 : Pre Calculus

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 #13 : Law Of Cosines And Sines

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 #1442 : Pre Calculus

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 #15 : Law Of Cosines And 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 #16 : Law Of Cosines And Sines

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 #13 : Law Of Cosines And Sines

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 #18 : Law Of Cosines And Sines

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...

Example Question #19 : Law Of Cosines And Sines

Triangle_700

Given  and , what is the measurement of  to the nearest degree?

Possible Answers:

Correct answer:

Explanation:

Using the information we have, we can solve for 

.

Plugging in what we know, we have: 

.

Then, solve for 

.

Simplify, then solve for  which means .

Therefore, after rounding to the nearest degree, .

To solve for , subtract  and  from .

Therefore, .

Example Question #61 : Trigonometric Applications

Find the length of the missing side, .

2

Possible Answers:

Correct answer:

Explanation:

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

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

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

 

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