### All SAT II Math I Resources

## Example Questions

### Example Question #1 : 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 #1 : 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 #1 : 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:

### Example Question #5 : Trigonometry

What is the measure of the angle made between a line segment with points , and the -axis? Round your answer to the nearest hundreth of a degree.

**Possible Answers:**

No angle measure can be calculated

**Correct answer:**

Based on the information given, we know that the ratio of to on this segment could be represented as:

This ratio represents the tangent of the triangle formed by our line segment and the -axis. Using the inverse tangent function, we can find the angle measure:

This refers to a reference angle of

### Example Question #1 : Trigonometry

What is the measure of the angle made between a line segment with points , and the -axis? Round your answer to the nearest hundreth of a degree.

**Possible Answers:**

No angle can be calculated

**Correct answer:**

Based on the information given, we know that the ratio of to on this segment could be represented as:

This ratio represents the tangent of the triangle formed by our line segment and the -axis. Using the inverse tangent function, we can find the angle measure:

This refers to a reference angle of .

### Example Question #7 : Trigonometry

A triangle is formed by connecting the points . Determine the elevation angle to the nearest integer in degrees.

**Possible Answers:**

**Correct answer:**

After connecting the points on the graph, the length of the triangular base is 1 unit.

The height of the triangle is 6. To find the elevation angle, the angle is opposite from the height of the triangle. Since we know the base and the height, the elevation angle can be solved by using the property of tangent.

The best answer is .

### Example Question #8 : Trigonometry

Solve for between .

**Possible Answers:**

**Correct answer:**

First we must solve for when sin is equal to 1/2. That is at

Now, plug it in:

### Example Question #9 : Trigonometry

Solve for between .

**Possible Answers:**

**Correct answer:**

First we must solve for when sin is equal to 1/2. That is at

Now, plug it in:

### Example Question #1 : Sine, Cosine, Tangent

In a triangle, , what is the measure of angle A if the side opposite of angle A is 3 and the adjacent side to angle A is 4?

(Round answer to the nearest tenth of a degree.)

**Possible Answers:**

**Correct answer:**

To find the measure of angle of A we will use tangent to solve for A. We know that

In our case opposite = 3 and adjacent = 4, we substitute these values in and get:

Now we take the inverse tangent of each side to find the degree value of A.

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