Question

the sides of a triangle are 56, 48, and 70. use the pythagorean theorem to determine if the triangle is right, acute, or obtuse.
answer
the triangle is acute because the square of the largest side is less than the sum of the squares of the other two sides.

Explanation:

Step1: Identify the largest side

The sides are 56, 48, and 70. The largest side is 70.

Step2: Calculate the square of the largest side

Calculate \(70^2 = 4900\).

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

Calculate \(56^2 + 48^2\). \(56^2 = 3136\) and \(48^2 = 2304\). Then \(3136 + 2304 = 5440\).

Step4: Compare the two results

Compare \(4900\) (square of largest side) with \(5440\) (sum of squares of other two sides). Since \(4900 < 5440\), by the Pythagorean inequality theorem, if \(c^2 < a^2 + b^2\) (where \(c\) is the largest side), the triangle is acute.

Answer:

The triangle is acute because the square of the largest side (70² = 4900) is less than the sum of the squares of the other two sides (56² + 48² = 5440).