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, 21
acute and isosceles:
anything from 11, 11, 1 to 11, 11, 15
obtuse 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, 61 is 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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