### All Trigonometry Resources

## Example Questions

### Example Question #1 : Law Of Sines

Given sides , and angle determine the corresponding value for

**Possible Answers:**

Undefined

**Correct answer:**

The Law of Sines is used here since we have Side - Angle - Side. We setup our equation as follows:

Next, we substitute the known values:

Now we cross multiply:

Divide by 10 on both sides:

Finally taking the inverse sine to obtain the desired angle:

### Example Question #1 : Law Of Sines

Let , and , determine the length of side .

**Possible Answers:**

**Correct answer:**

We have two angles and one side, however we do not have . We can determine the angle using the property of angles in a triangle summing to :

Now we can simply utilize the Law of Sines:

Cross multiply and divide:

Reducing to obtain the final solution:

### Example Question #3 : Law Of Sines

In the above triangle, and . If , what is to the nearest tenth? (note: triangle not to scale)

**Possible Answers:**

**Correct answer:**

If we solve for , we can use the Law of Sines to find .

Since the sum of angles in a triangle equals ,

Now, using the Law of Sines:

### Example Question #1 : Law Of Sines

By what factor is larger than in the triangle pictured above.

**Possible Answers:**

It isn't

**Correct answer:**

The Law of Sines states

so for a and b, that sets up

### Example Question #1 : Law Of Sines

Solve for :

**Possible Answers:**

**Correct answer:**

To solve, use the law of sines, where a is the side across from the angle A, and b is the side across from the angle B.

cross-multiply

evaluate the right side

divide by 7

take the inverse sine

### Example Question #1 : Law Of Sines

Evaluate using law of sines:

**Possible Answers:**

**Correct answer:**

To solve, use law of sines, where side a is across from angle A, and side b is across from angle B.

In this case, we have a 90-degree angle across from x, but we don't currently know the angle across from the side length 7. We can figure out this angle by subtracting from :

Now we can set up and solve using law of sines:

cross-multiply

evaluate the sines

divide by 0.9063

### Example Question #31 : Law Of Cosines And Law Of Sines

What is the measure of in below? Round to the nearest tenth of a degree.

**Possible Answers:**

**Correct answer:**

The law of sines tells us that , where *a*, *b*, and *c* are the sides opposite of angles *A*, *B*, and *C*. In , these ratios can be used to find :

### Example Question #1 : Law Of Sines

Find the length of the line segment in the triangle below.

Round to the nearest hundredth of a centimeter.

**Possible Answers:**

**Correct answer:**

The law of sines states that

.

In this triangle, we are looking for the side length *c*, and we are given angle *A*, angle *B*, and side *b*. The sum of the interior angles of a triangle is ; using subtraction we find that angle *C* = .

We can now form a proportion that includes only one unknown, *c*:

Solving for *c*, we find that

.

### Example Question #1 : Law Of Sines

In the triangle below, , , and . What is the length of side to the nearest tenth?

**Possible Answers:**

**Correct answer:**

First, find . The sum of the interior angles of a triangle is , so , or .

Using this information, you can set up a proportion to find side *b*:

### Example Question #1 : Law Of Sines

In the triangle below, , , and .

What is the length of side *a* to the nearest tenth?

**Possible Answers:**

**Correct answer:**

To use the law of sines, first you must find the measure of . Since the sum of the interior angles of a triangle is , .

Law of sines: