Find the missing angle according to the Triangle Exterior Angle Theorem
2 answers:
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Refer to the figure shown below.
We shall review each of the three given measurements and decide what type of triangle we have.
Measurement a.
a=3, b=4, c=5.
For a right triangle, c² = a² + b² (Pythagorean theorem)
a² + b² = 3² + 4² = 9 + 16 = 25
c² = 5² = 25
Answer:
This is a right triangle, because c² = a² + b².
Measurement b.
a=5, b=6, c=7.
For an acute triangle, c² < a² + b².
a² + b² = 5² + 6² = 25 + 36 = 61
c² = 7² = 49
Answer:
This is an acute triangle, because c² < a² + b².
Measurement c.
a=8, b=9, c=12.
For an obtuse triangle, c² > a² + b².
a² + b² = 8² + 9² = 64 + 81 = 145
c² = 12² = 144
Answer:
This is an acute triangle because c² < a² + b².
We shall review each of the three given measurements and decide what type of triangle we have.
Measurement a.
a=3, b=4, c=5.
For a right triangle, c² = a² + b² (Pythagorean theorem)
a² + b² = 3² + 4² = 9 + 16 = 25
c² = 5² = 25
Answer:
This is a right triangle, because c² = a² + b².
Measurement b.
a=5, b=6, c=7.
For an acute triangle, c² < a² + b².
a² + b² = 5² + 6² = 25 + 36 = 61
c² = 7² = 49
Answer:
This is an acute triangle, because c² < a² + b².
Measurement c.
a=8, b=9, c=12.
For an obtuse triangle, c² > a² + b².
a² + b² = 8² + 9² = 64 + 81 = 145
c² = 12² = 144
Answer:
This is an acute triangle because c² < a² + b².