# SAT II Math II : Law of Cosines

## Example Questions

### 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)?

Explanation:

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)?

Explanation:

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 #3 : Law Of Cosines

Given : with .

Which of the following whole numbers is closest to ?

Explanation:

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.

The correct answer is not given among the other responses.

Explanation:

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.

Explanation:

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: