Question

the sides of a triangle are 30, 64, and 90. 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 and calculate its square

The largest side is 90. Its square is $90^2=8100$.

Step2: Calculate the sum of the squares of the other two sides

The other two sides are 30 and 64. Their squares are $30^2 = 900$ and $64^2=4096$. The sum is $900 + 4096=4996$.

Step3: Compare the two - values

Since $8100>4996$ (i.e., the square of the largest side is greater than the sum of the squares of the other two sides), the triangle is obtuse.

Answer:

The triangle is obtuse because the square of the largest side is greater than the sum of the squares of the other two sides.