Part A) In all the following problems where triangles are defined by lengths, we will use the number 11 and the other numbers must be whole numbers.

obtuse and isosceles: 11, 11, _____

acute and isosceles: 11, 11, _____

obtuse and scalene: 11, ___, ___

right and scalene: 11, ____, ____ (hint: 11 will be one of the legs.)

acute and scalene: 11, ____, ____

Part B) In all the following problems where triangles are defined by angles, we will use one angle of 34° and the other numbers must be whole numbers.

obtuse and isosceles: 34°, ____, _____

acute and isosceles: 34°, ____, _____

obtuse and scalene: 34°, ___, _____ (many correct answers.)

right and scalene: 34°, ____, ____

acute and scalene: 34°, ____, ____ (many correct answers.)

Answers in the comments.

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Part A) In all the following problems where triangles are defined by lengths, we will use the number 11 and the other numbers must be whole numbers.

obtuse and isosceles:

anything from 11, 11, 16 to 11, 11, 21acute and isosceles:

anything from 11, 11, 1 to 11, 11, 15obtuse and scalene:

11, 12, 17 (many possible answers)right and scalene: 11, ____, ____ (hint: 11 will be one of the legs.)

we want a² + 11² = (a+1)². When we do the math, this means

a² + 121 = a² + 2a + 1, so

121 = 2a + 1

120 = 2a

60 = a

11, 60, 61is a right triangle.acute and scalene:

11, 12, 13 is one of many correct answers.Part B) In all the following problems where triangles are defined by angles, we will use one angle of 34° and the other numbers must be whole numbers.

obtuse and isosceles:

34°, 34°, 112°acute and isosceles:

34°, 73°, 73°obtuse and scalene:

34°, 100°, 46°(many correct answers.)

right and scalene:

34°, 56°, 90°acute and scalene:

34°, 80°, 66°(many correct answers.)

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