# Precalculus : Law of Cosines and Sines

## Example Questions

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

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

Solve for . Round to the nearest tenth.

None of these answers are correct.

Explanation:

Law of Cosines

Therefore...

After rounding...

### Example Question #1441 : Pre Calculus

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

(Not drawn to scale.)

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 .

(Not drawn to scale.)

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?

None of the above

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?

None of the above

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:

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.

Solve for . Round to the nearest tenth.

None of these answers are correct.

Explanation:

Law of Sines

Therefore...

After rounding...

### Example Question #18 : Law Of Cosines And Sines

Solve for c using Law of Sines, given:

Round to the nearest tenth.

None of these answers are correct.

Explanation:

Law of Sines

Therefore...

After rounding...

### Example Question #19 : Law Of Cosines And Sines

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

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, .