### All SAT II Math II Resources

## Example Questions

### Example Question #1 : Radians And The Unit Circle

The degree angle can be expressed as what in radians?

**Possible Answers:**

**Correct answer:**

In order to convert degrees to radians, we will need to know the conversion factor.

Set up a dimensional analysis to solve.

The answer is:

### Example Question #2 : Radians And The Unit Circle

Which of the following angles belong in the fourth quadrant?

**Possible Answers:**

**Correct answer:**

The fourth quadrant is in the positive x-axis and negative y-axis.

The angle ranges are:

The only possible answer is:

### Example Question #3 : Radians And The Unit Circle

What degree measure is equivalent to ?

**Possible Answers:**

**Correct answer:**

Every pi radians is equal to 180 degrees.

Replace the pi term with 180 degrees and multiply.

The answer is:

### Example Question #1 : Law Of Cosines

A triangle has sides that measure 10, 12, and 16. What is the greatest measure of any of its angles (nearest tenth of a degree)?

**Possible Answers:**

**Correct answer:**

We are seeking the measure of the angle opposite the side of greatest length, 16.

We can use the Law of Cosines, setting , and solving for :

### Example Question #2 : Law Of Cosines

A triangle has sides that measure 15, 17, and 30. What is the least measure of any of its angles (nearest tenth of a degree)?

**Possible Answers:**

**Correct answer:**

We are seeking the measure of the angle opposite the side of least length, 15.

We can use the Law of Cosines, setting , and solving for :

### Example Question #1 : Law Of Cosines

Given : with .

Which of the following whole numbers is closest to ?

**Possible Answers:**

**Correct answer:**

Apply the Law of Cosines

setting and solving for :

Of the five choices, 27 comes closest.

### Example Question #2 : Law Of Cosines

Given : with .

Evaluate to the nearest tenth.

**Possible Answers:**

The correct answer is not given among the other responses.

**Correct answer:**

Apply the Law of Cosines

setting and solving for :

### Example Question #5 : Law Of Cosines

In :

Evaluate the length of to the nearest tenth of a unit.

**Possible Answers:**

**Correct answer:**

The figure referenced is below:

By the Law of Cosines, given the lengths and of two sides of a triangle, and the measure of their included angle, the length of the third side can be calculated using the formula

Substituting , , , and , then evaluating:

Taking the square root of both sides:

### Example Question #1 : Law Of Sines

Find the measure of angle .

**Possible Answers:**

**Correct answer:**

Start by using the Law of Sines to find the measure of angle .

Since the angles of a triangle must add up to ,

### Example Question #1 : Law Of Sines

In ,

Evaluate (nearest degree)

**Possible Answers:**

Cannot be determined

**Correct answer:**

Cannot be determined

By the Law of Sines, if and are the lengths of two sides of a triangle, and and the measures of their respective opposite angles,

and are opposite sides and , so, setting , , , and :

However, the range of the sine function is , so there is no value of for which this is true. Therefore, this triangle cannot exist.

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