### All High School Math Resources

## Example Questions

### Example Question #1 : Triangles

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

**Possible Answers:**

**Correct answer:**

For this problem, use the law of sines:

.

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

Cross multiply:

Multiply both sides by :

### Example Question #2 : Triangles

In this figure and . If , what is ?

**Possible Answers:**

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

**Possible Answers:**

**Correct answer:**

Since we are given and want to find , we apply the Law of Sines, which states, in part,

and

Substitute in the above equation:

Cross-multiply and solve for :

### Example Question #2 : Applying The Law Of Sines

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

**Possible Answers:**

No triangle can exist with these characteristics.

**Correct answer:**

Since we are given , , and , and want to find , we apply the Law of Sines, which states, in part,

.

Substitute and solve for :

Take the inverse sine of 0.6355:

There are two angles between and that have any given positive sine other than 1 - we get the other by subtracting the previous result from :

This, however, is impossible, since this would result in the sum of the triangle measures being greater than . This leaves as the only possible answer.

### Example Question #3 : 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 #4 : Graphs And Inverses Of Trigonometric Functions

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: