# Common Core: High School - Geometry : Apply Laws of Sines and Cosines: CCSS.Math.Content.HSG-SRT.D.11

## Example Questions

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### Example Question #1 : Apply Laws Of Sines And Cosines: Ccss.Math.Content.Hsg Srt.D.11

To the nearest hundredth, solve  where, , , and .

Explanation:

The first step is to create a picture

Since we have 2 angles, we can solve for the 3rd angle easily.

Now we can use the Law of Sines to figure out one side

Recall the Law of Sines

Now plug in 11 for B , 71 for A and 179 for a , and solve for the missing side.

Remember to round to the nearest hundredth.

Now we need to solve for the last side of the triangle.

To solve for this, we can use the Law of Cosines.

Lets recall the Law of Cosines.

### Example Question #2 : Apply Laws Of Sines And Cosines: Ccss.Math.Content.Hsg Srt.D.11

To the nearest hundredth, solve  where, , , and .

Explanation:

The first step is to create a picture

Since we have 2 angles, we can solve for the 3rd angle easily.

Now we can use the Law of Sines to figure out one side

Recall the Law of Sines

Now plug in 18 for B , 66 for A and 78 for a , and solve for the missing side.

Remember to round to the nearest hundredth.

Now we need to solve for the last side of the triangle.

To solve for this, we can use the Law of Cosines.

Lets recall the Law of Cosines.

### Example Question #3 : Apply Laws Of Sines And Cosines: Ccss.Math.Content.Hsg Srt.D.11

To the nearest hundredth, solve  where, , , and .

Explanation:

The first step is to create a picture

Since we have 2 angles, we can solve for the 3rd angle easily.

Now we can use the Law of Sines to figure out one side

Recall the Law of Sines

Now plug in 32 for B , 82 for A and 95 for a , and solve for the missing side.

Remember to round to the nearest hundredth.

Now we need to solve for the last side of the triangle.

To solve for this, we can use the Law of Cosines.

Lets recall the Law of Cosines.

### Example Question #4 : Apply Laws Of Sines And Cosines: Ccss.Math.Content.Hsg Srt.D.11

To the nearest hundredth, solve  where, , , and .

Explanation:

The first step is to create a picture

Since we have 2 angles, we can solve for the 3rd angle easily.

Now we can use the Law of Sines to figure out one side

Recall the Law of Sines

Now plug in 3 for B , 81 for A and 182 for a , and solve for the missing side.

Remember to round to the nearest hundredth.

Now we need to solve for the last side of the triangle.

To solve for this, we can use the Law of Cosines.

Lets recall the Law of Cosines.

### Example Question #5 : Apply Laws Of Sines And Cosines: Ccss.Math.Content.Hsg Srt.D.11

To the nearest hundredth, solve  where, , , and .

Explanation:

The first step is to create a picture

Since we have 2 angles, we can solve for the 3rd angle easily.

Now we can use the Law of Sines to figure out one side

Recall the Law of Sines

Now plug in 29 for B , 108 for A and 131 for a , and solve for the missing side.

Remember to round to the nearest hundredth.

Now we need to solve for the last side of the triangle.

To solve for this, we can use the Law of Cosines.

Lets recall the Law of Cosines.

### Example Question #6 : Apply Laws Of Sines And Cosines: Ccss.Math.Content.Hsg Srt.D.11

To the nearest hundredth, solve  where,  , , and .

Explanation:

The first step is to create a picture

Since we have 2 angles, we can solve for the 3rd angle easily.

Now we can use the Law of Sines to figure out one side

Recall the Law of Sines

Now plug in 27 for B , 120 for A and 116 for a , and solve for the missing side.

Remember to round to the nearest hundredth.

Now we need to solve for the last side of the triangle.

To solve for this, we can use the Law of Cosines.

Lets recall the Law of Cosines.

### Example Question #7 : Apply Laws Of Sines And Cosines: Ccss.Math.Content.Hsg Srt.D.11

To the nearest hundredth, solve  where, , , and .

Explanation:

The first step is to create a picture

Since we have 2 angles, we can solve for the 3rd angle easily.

Now we can use the Law of Sines to figure out one side

Recall the Law of Sines

Now plug in 27 for B , 123 for A and 111 for a , and solve for the missing side.

Remember to round to the nearest hundredth.

Now we need to solve for the last side of the triangle.

To solve for this, we can use the Law of Cosines.

Lets recall the Law of Cosines.

### Example Question #8 : Apply Laws Of Sines And Cosines: Ccss.Math.Content.Hsg Srt.D.11

To the nearest hundredth, solve  where, , , and .

Explanation:

The first step is to create a picture

Since we have 2 angles, we can solve for the 3rd angle easily.

Now we can use the Law of Sines to figure out one side

Recall the Law of Sines

Now plug in 15 for B , 97 for A and 100 for a , and solve for the missing side.

Remember to round to the nearest hundredth.

Now we need to solve for the last side of the triangle.

To solve for this, we can use the Law of Cosines.

Lets recall the Law of Cosines.

### Example Question #9 : Apply Laws Of Sines And Cosines: Ccss.Math.Content.Hsg Srt.D.11

To the nearest hundredth, solve  where, , , and .

Explanation:

The first step is to create a picture

Since we have 2 angles, we can solve for the 3rd angle easily.

Now we can use the Law of Sines to figure out one side

Recall the Law of Sines

Now plug in 16 for B , 43 for A and 109 for a , and solve for the missing side.

Remember to round to the nearest hundredth.

Now we need to solve for the last side of the triangle.

To solve for this, we can use the Law of Cosines.

Lets recall the Law of Cosines.

### Example Question #10 : Apply Laws Of Sines And Cosines: Ccss.Math.Content.Hsg Srt.D.11

To the nearest hundredth, solve  where, , , and .

Explanation:

The first step is to create a picture

Since we have 2 angles, we can solve for the 3rd angle easily.

Now we can use the Law of Sines to figure out one side

Recall the Law of Sines

Now plug in 2 for B , 79 for A and 99 for a , and solve for the missing side.

Remember to round to the nearest hundredth.

Now we need to solve for the last side of the triangle.

To solve for this, we can use the Law of Cosines.

Lets recall the Law of Cosines.

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