# High School Math : Applying the Law of Sines

## Example Questions

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

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

Explanation:

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 : Applying The Law Of Sines

In this figure  and . If , what is ?

Explanation:

For this problem, use the law of sines:

.

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

### Example Question #3 : Applying The Law Of Sines

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

Explanation:

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 #4 : Applying The Law Of Sines

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

No triangle can exist with these characteristics.

Explanation:

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 #13 : Triangles

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 #14 : Triangles

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: