# High School Math : Right Triangles

## Example Questions

### Example Question #1 : Applying Trigonometric Functions

In this figure, side , and . What is the value 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 #2 : Applying Trigonometric Functions

Let ABC be a right triangle with sides  = 3 inches,  = 4 inches, and  = 5 inches. In degrees, what is the  where  is the angle opposite of side ?

Explanation:

We are looking for . Remember the definition of  in a right triangle is the length of the opposite side divided by the length of the hypotenuse.

So therefore, without figuring out  we can find

### Example Question #3 : Applying Trigonometric Functions

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 #5 : 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 #6 : 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 ?