Determine if the segment lengths form a triangle. if so, would the triangle be acute, right, or obtuse? 4.1, 8.2, 12.2
a. no, they do not form a triangle.
b. yes, they would form an acute triangle.
c. yes, they would form a right triangle.
d. yes, they would form an obtuse triangle

Using the given lengths of the triangle which are, 4.1, 8.2, and 12.2, the correct answer would be D. Yes, they would form an obtuse triangle.

In this problem, we apply the Pythagorean Theorem that the square of the hypotenus or the longest side of the triangle is equal to the sum of the squares of both legs. In this case, the hypotenus would be 12.2 and the remaining two would be the legs of the triangle.

If 12.2^2 = 4.1^2 + 8.2^2, then it is a right triangle.
If 12.2^2 < 4.1^2 + 8.2^2, then it is an acute triangle.
If 12.2^2 > 4.1^2 + 8.2^2, then it is an obtuse triangle.

Having this in mind, let's solve for their squares.

12.2^ = 4.1^2 + 8.2^2
148.84 = 16.81 + 67.24
148.84 = 84.05
148.84 > 84.05

So the answer would be that it is an obtuse triangle.