# Precalculus : Pre-Calculus

## Example Questions

### Example Question #1 : Trigonometry

What is  if  and ?

Explanation:

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

Not enough information to solve

Explanation:

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?

Explanation:

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

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

Undefined

Explanation:

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.)

Undefined

Explanation:

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 ?

Undefined

Explanation:

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 ?

Undefined

Explanation:

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 ?

Explanation:

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?

Explanation:

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 ?

A triangle with these characteristics cannot exist.