Problem 5 Classifying a Triangle

A triangle has side lengths 6, 11, and 14. Is it acute, obtuse, or right?

c 2 □ a 2 + b 2 Compare  c 2  to  a 2 + b 2 . 14 2 □ 6 2 + 11 2 Substitute the greatest value for  c . 196 □ 36 + 121 Simplify . 196 > 157     table with 4 rows and 3 columns , row1 column 1 , c squared , white square , eh squared , column 2 plus , b squared , column 3 cap compare . c squared , to , eh squared , plus , b squared , . , row2 column 1 , 14 squared , white square , 6 squared , column 2 plus , 11 squared , column 3 cap substitutethegreatestvaluefor . c . , row3 column 1 , 196 white square 36 , column 2 plus 121 , column 3 cap simplify , . , row4 column 1 , 196 greater than 157 , column 2 , column 3 , end table

Since c 2 > a 2 + b 2 , c squared , greater than , eh squared , plus , b squared , comma the triangle is obtuse.

✓ Got It?

5. Is a triangle with side lengths 7, 8, and 9 acute, obtuse, or right?

✓ Lesson Check

Do you know HOW?

What is the value of x in simplest radical form?

Do you UNDERSTAND?

5. Vocabulary Describe the conditions that a set of three numbers must meet in order to form a Pythagorean triple.

6. Error Analysis A triangle has side lengths 16, 34, and 30. Your friend says it is not a right triangle. Look at your friend's work and describe the error.