5. given the following triangle side lengths, identify the triangle as acute, right or obtuse. show your work.
a. 3in, 4in, 5 in
b. 5in, 6in, 7in
c. 8in, 9in, 12in

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

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

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

This is an acute triangle because c² < a² + b².

The answer is "a"radius = 12.7 unitsdiameter = radius × 212.7 units × 2 = 25.4 units

This does not make sense