Question

the sides of a triangle are 30, 24, and 18. use the pythagorean theorem to determine if the triangle is right, acute, or obtuse.
answer
the triangle is because the square of the largest side the sum of the squares of the other two sides.

Explanation:

Step1: Identify the largest side

The largest side is 30.

Step2: Calculate the square of the largest side

$30^2=900$.

Step3: Calculate the sum of the squares of the other two sides

$24^2 + 18^2=576+324 = 900$.

Step4: Compare the values

Since $30^2=24^2 + 18^2$, by the Pythagorean - Theorem converse, the triangle is a right - triangle.

Answer:

The triangle is right because the square of the largest side equals the sum of the squares of the other two sides.