### All Precalculus Resources

## Example Questions

### Example Question #11 : Use The Laws Of Cosines And Sines

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

Solve for . Round to the nearest tenth.

**Possible Answers:**

None of these answers are correct.

**Correct answer:**

Law of Cosines

Therefore...

After rounding...

### Example Question #12 : Use The Laws Of Cosines And Sines

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

*(Not drawn to scale.)*

**Possible Answers:**

**Correct answer:**

We use the Law of Sines to solve this problem

we plug in

solving for we get:

### Example Question #13 : Use The Laws Of Cosines And Sines

Use the Law of Sines to find .

* *

*(Not drawn to scale.)*

**Possible Answers:**

**Correct answer:**

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 #14 : Use The Laws Of Cosines And Sines

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

**Possible Answers:**

None of the above

**Correct answer:**

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 : Use The Laws Of Cosines And Sines

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

**Possible Answers:**

None of the above

**Correct answer:**

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 : Use The Laws Of Cosines And Sines

Solve the triangle using the Law of Sines:

**Possible Answers:**

None of the other answers

**Correct answer:**

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 #17 : Use The Laws Of Cosines And Sines

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

Solve for . Round to the nearest tenth.

**Possible Answers:**

None of these answers are correct.

**Correct answer:**

Law of Sines

Therefore...

After rounding...

### Example Question #18 : Use The Laws Of Cosines And Sines

Solve for c using Law of Sines, given:

Round to the nearest tenth.

**Possible Answers:**

None of these answers are correct.

**Correct answer:**

Law of Sines

Therefore...

After rounding...

### Example Question #19 : Use The Laws Of Cosines And Sines

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

**Possible Answers:**

**Correct answer:**

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 #20 : Use The Laws Of Cosines And Sines

Find the length of the missing side, .

**Possible Answers:**

**Correct answer:**

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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