### All SAT II Math I Resources

## Example Questions

### Example Question #1 : Finding Sides With Trigonometry

A plane flies degrees north of east for miles. It then turns and flies degrees south of east for miles. Approximately how many miles is the plane from its starting point? (Ignore the curvature of the Earth.)

**Possible Answers:**

**Correct answer:**

The plane flies two sides of a triangle. The angle formed between the two sides is 40 degrees. In a Side-Angle-Side situation, it is appropriate to employ the use of the Law of Cosines.

### Example Question #2 : Finding Sides With Trigonometry

In :

Evaluate to the nearest degree.

**Possible Answers:**

Insufficient information is provided to answer the question.

**Correct answer:**

The figure referenced is below:

By the Law of Cosines, the relationship of the measure of an angle of a triangle and the three side lengths , , and , the sidelength opposite the aforementioned angle, is as follows:

All three sidelengths are known, so we are solving for . Setting

. the length of the side opposite the unknown angle;

;

;

and ,

We get the equation

Solving for :

Taking the inverse cosine:

,

the correct response.

### Example Question #1 : Finding Sides With Trigonometry

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 #2 : Finding Sides With Trigonometry

In :

**Possible Answers:**

**Correct answer:**

The figure referenced is below:

The Law of Sines states that given two angles of a triangle with measures , and their opposite sides of lengths , respectively,

,

or, equivalently,

.

In this formula, we set:

, the desired sidelength;

, the measure of its opposite angle;

, the known sidelength;

, the measure of its opposite angle, which is

Substituting in the Law of Sines formula and solving for :

Evaluating the sines, then calculating:

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