SOLUTION: A triangle has one side that measures 3 ft, one side that measures 8 ft, and one side that measures 9 ft. What kind of triangle is it?

Question 940544: A triangle has one side that measures 3 ft, one side that measures 8 ft, and one side that measures 9 ft.
What kind of triangle is it?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
To begin with, we can call that triangle ,
meaning that its sides have different lengths.
However, I suspect you are expected to decide if the triangle is a right triangle, an acute triangle, or an obtuse triangle.

The largest angle in a triangle is the angle opposite the longest side.
If the angle opposite the side measuring 9 ft were a right angle,
the triangle would be a right triangle;
the longest side (9 ft) would be the hypotenuse,
and the other two sides would be the legs of that right triangle.

In a right triangle with legs measuring 3 ft and 8 ft,
the length (in ft) of the hypotenuse is
.

If the length of third side of your triangle were ft,
the triangle would be a right triangle, but ,
so the triangle is not a right triangle,
and the angle opposite the 9-ft side is not a right angle.

Is it larger than a right angle (an obtuse angle),
or is it smaller than a right angle (an acute angle)

, so the longest side is longer than ft.
Since the largest side is longer than needed for a right triangle with legs measuring 3 ft and 8 ft,
the largest angle is larger than a right angle: it is an obtuse angle.
So the triangle is an triangle.
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