# Common Core: High School - Geometry : Use Trigonometric Ratios and Pythagorean Theorem to Solve Right Triangles: CCSS.Math.Content.HSG-SRT.C.8

## Example Questions

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### Example Question #41 : Similarity, Right Triangles, & Trigonometry

Determine whether a triangle with side lengths 4 , 5 , and 3 is a right triangle.

Yes

No

No

Explanation:

To figure this problem out, we need to recall the Pythagorean Theorem.

Now we simply plug in 4 for , 5 for , and 3 for .

If both sides are equal, then the side lengths result in a right triangle.

Since both sides are not equal, we can conclude that the side lengths are not a right triangle.

### Example Question #1 : Use Trigonometric Ratios And Pythagorean Theorem To Solve Right Triangles: Ccss.Math.Content.Hsg Srt.C.8

Determine whether a triangle with side lengths  ,  , and  is a right triangle.

No

Yes

No

Explanation:

To figure this problem out, we need to recall the Pythagorean Theorem.

Now we simply plug in  for ,  for , and  for .

If both sides are equal, then the side lengths result in a right triangle.

Since both sides are not equal, we can conclude that the side lengths are not a right triangle.

### Example Question #1 : Use Trigonometric Ratios And Pythagorean Theorem To Solve Right Triangles: Ccss.Math.Content.Hsg Srt.C.8

Determine whether a triangle with side lengths  ,  , and  is a right triangle.

Yes

No

No

Explanation:

To figure this problem out, we need to recall the Pythagorean Theorem.

Now we simply plug in  for ,  for , and  for .

If both sides are equal, then the side lengths result in a right triangle.

Since both sides are not equal, we can conclude that the side lengths are not a right triangle.

### Example Question #2 : Use Trigonometric Ratios And Pythagorean Theorem To Solve Right Triangles: Ccss.Math.Content.Hsg Srt.C.8

Determine whether a triangle with side lengths  ,  , and  is a right triangle.

Yes

No

No

Explanation:

To figure this problem out, we need to recall the Pythagorean Theorem.

Now we simply plug in  for ,  for , and  for .

If both sides are equal, then the side lengths result in a right triangle.

Since both sides are not equal, we can conclude that the side lengths are not a right triangle.

### Example Question #1 : Use Trigonometric Ratios And Pythagorean Theorem To Solve Right Triangles: Ccss.Math.Content.Hsg Srt.C.8

Determine whether a triangle with side lengths  ,  , and  is a right triangle.

Yes

No

No

Explanation:

To figure this problem out, we need to recall the Pythagorean Theorem.

Now we simply plug in  for ,  for , and  for .

If both sides are equal, then the side lengths result in a right triangle.

Since both sides are not equal, we can conclude that the side lengths are not a right triangle.

### Example Question #4 : Use Trigonometric Ratios And Pythagorean Theorem To Solve Right Triangles: Ccss.Math.Content.Hsg Srt.C.8

Determine whether a triangle with side lengths  ,  , and  is a right triangle.

Yes

No

Yes

Explanation:

To figure this problem out, we need to recall the Pythagorean Theorem.

Now we simply plug in  for ,  for , and  for .

If both sides are equal, then the side lengths result in a right triangle.

Since both sides are equal, we can conclude that the side lengths are a right triangle.

### Example Question #53 : Similarity, Right Triangles, & Trigonometry

Determine whether a triangle with side lengths  ,  , and  is a right triangle.

Yes

No

No

Explanation:

To figure this problem out, we need to recall the Pythagorean Theorem.

Now we simply plug in  for ,  for , and  for c.

If both sides are equal, then the side lengths result in a right triangle.

Since both sides are not equal, we can conclude that the side lengths are not a right triangle.

### Example Question #1 : Use Trigonometric Ratios And Pythagorean Theorem To Solve Right Triangles: Ccss.Math.Content.Hsg Srt.C.8

Determine whether a triangle with side lengths  ,  , and  is a right triangle.

No

Yes

No

Explanation:

To figure this problem out, we need to recall the Pythagorean Theorem.

Now we simply plug in  for ,  for , and  for .

If both sides are equal, then the side lengths result in a right triangle.

Since both sides are not equal, we can conclude that the side lengths are not a right triangle.

### Example Question #1 : Use Trigonometric Ratios And Pythagorean Theorem To Solve Right Triangles: Ccss.Math.Content.Hsg Srt.C.8

Determine whether a triangle with side lengths  ,  , and  is a right triangle.

Yes

No

No

Explanation:

To figure this problem out, we need to recall the Pythagorean Theorem.

Now we simply plug in  for ,  for , and  for .

If both sides are equal, then the side lengths result in a right triangle.

Since both sides are not equal, we can conclude that the side lengths are not a right triangle.

### Example Question #54 : Similarity, Right Triangles, & Trigonometry

Determine whether a triangle with side lengths  ,  , and  is a right triangle.

No

Yes

No

Explanation:

To figure this problem out, we need to recall the Pythagorean Theorem.

Now we simply plug in  for ,  for , and  for .

If both sides are equal, then the side lengths result in a right triangle.

Since both sides are not equal, we can conclude that the side lengths are not a right triangle.

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