### All Precalculus Resources

## Example Questions

### Example Question #1 : Trigonometry

What is if and ?

**Possible Answers:**

**Correct answer:**

In order to find we need to utilize the given information in the problem. We are given the opposite and adjacent sides. We can then, by definition, find the of and its measure in degrees by utilizing the function.

Now to find the measure of the angle using the function.

If you calculated the angle's measure to be then your calculator was set to radians and needs to be set on degrees.

### Example Question #3 : Graphs And Inverses Of Trigonometric Functions

If equals and is , how long is ?

**Possible Answers:**

Not enough information to solve

**Correct answer:**

This problem can be easily solved using trig identities. We are given the hypotenuse and . We can then calculate side using the .

Rearrange to solve for .

If you calculated the side to equal then you utilized the function rather than the .

### Example Question #4 : Graphs And Inverses Of Trigonometric Functions

What is the length of CB?

**Possible Answers:**

**Correct answer:**

### Example Question #5 : Graphs And Inverses Of Trigonometric Functions

In this figure, angle . If side and , what is the value of angle ?

**Possible Answers:**

Undefined

**Correct answer:**

For this problem, use the law of sines:

.

In this case, we have values that we can plug in:

### Example Question #1 : Applying The Law Of Sines

In this figure, if angle , side , and side , what is the value of angle ?

(NOTE: Figure not necessarily drawn to scale.)

**Possible Answers:**

Undefined

**Correct answer:**

First, observe that this figure is clearly not drawn to scale. Now, we can solve using the law of sines:

.

In this case, we have values that we can plug in:

### Example Question #1 : Triangles

In this figure, if angle , side , and side , what is the measure of angle ?

**Possible Answers:**

Undefined

**Correct answer:**

Since , we know we are working with a right triangle.

That means that .

In this problem, that would be:

Plug in our given values:

### Example Question #7 : Graphs And Inverses Of Trigonometric Functions

In this figure, , , and . What is the value of angle ?

**Possible Answers:**

Undefined

**Correct answer:**

Notice that these sides fit the pattern of a 30:60:90 right triangle: .

In this case, .

Since angle is opposite , it must be .

### Example Question #8 : Graphs And Inverses Of Trigonometric Functions

A triangle has angles of . If the side opposite the angle is , what is the length of the side opposite ?

**Possible Answers:**

**Correct answer:**

The pattern for is that the sides will be .

If the side opposite is , then the side opposite will be .

### Example Question #11 : Graphs And Inverses Of Trigonometric Functions

A triangle has sides of length 12, 17, and 22. Of the measures of the three interior angles, which is the greatest of the three?

**Possible Answers:**

**Correct answer:**

We can apply the Law of Cosines to find the measure of this angle, which we will call :

The widest angle will be opposite the side of length 22, so we will set:

, ,

### Example Question #12 : Graphs And Inverses Of Trigonometric Functions

In , , , and . To the nearest tenth, what is ?

**Possible Answers:**

A triangle with these characteristics cannot exist.

**Correct answer:**

By the Law of Cosines:

or, equivalently,

Substitute:

Certified Tutor