A triangle has side lengths of 18 cm, 80 cm, and 81 cm. Is the triangle acute, obtuse, or right?
To determine whether a triangle is acute, obtuse, or right, we can use the Pythagorean theorem.
Let's label the sides of the triangle as follows:
- Side a = 18 cm
- Side b = 80 cm
- Side c = 81 cm
Now, we'll find the square of each side:
- a^2 = 18^2 = 324
- b^2 = 80^2 = 6400
- c^2 = 81^2 = 6561
Next, we'll arrange the sides in ascending order:
324, 6400, 6561
According to the Pythagorean theorem, for a triangle to be right-angled, the square of the longest side must be equal to the sum of the squares of the other two sides. In this case, 6561 (c^2) does not equal 324 + 6400 (a^2 + b^2).
Since 6561 is greater than 324 + 6400, the triangle is obtuse.