Asked by Emily Monae

A triangle has side lengths of 18 cm, 80 cm, and 81 cm. Is the triangle acute, obtuse, or right?

Answers

There are no human answers yet.
Answered by GPT 3.5
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.