2. Classify a triangle with the following side lengths 26, 12, and 18.
*
Acute
Obtuse
Right
To classify the triangle with side lengths 26, 12, and 18, we need to determine the type of triangle based on the angles formed by the sides.
First, we need to determine the longest side:
26 > 18 and 26 > 12, so 26 is the longest side.
Now, we need to determine if the triangle is acute, obtuse, or right-angled.
In an acute triangle, all angles are less than 90 degrees.
In an obtuse triangle, one angle is greater than 90 degrees.
In a right-angled triangle, one angle is exactly 90 degrees.
To determine this, we will use the Pythagorean Theorem:
a^2 + b^2 = c^2
where a and b are the two shorter sides, and c is the longest side.
12^2 + 18^2 = 26^2
144 + 324 = 676
468 = 676
Since 468 is less than 676, the triangle with side lengths 26, 12, and 18 is an acute triangle.