SAT II Math II : Law of Cosines

Study concepts, example questions & explanations for SAT II Math II

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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)?

Possible Answers:

Correct answer:

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)?

Possible Answers:

Correct answer:

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 #2 : Law Of Cosines

Given : with .

Which of the following whole numbers is closest to ?

Possible Answers:

Correct answer:

Explanation:

Apply the Law of Cosines

setting  and solving for :

Of the five choices, 27 comes closest.

Example Question #4 : Law Of Cosines

Given : with .

Evaluate  to the nearest tenth.

Possible Answers:

The correct answer is not given among the other responses.

Correct answer:

Explanation:

Apply the Law of Cosines

setting  and solving for :

Example Question #3 : Law Of Cosines

In :

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

Possible Answers:

Correct answer:

Explanation:

The figure referenced is below:

Triangle 2

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:

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