# 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 #1 : 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 #1 : 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 #11 : Trigonometry

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 #462 : Sat Subject Test In Math Ii

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: ### All SAT II Math II Resources 